LMFDB - Embedded newform 29.7.c.a.12.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,7,Mod(12,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.67156842498$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.1
Character	$\chi$	$=$	29.12
Dual form			29.7.c.a.17.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.1386 - 11.1386i) q^{2} +(25.3142 + 25.3142i) q^{3} +184.138i q^{4} -151.054i q^{5} -563.931i q^{6} -332.137 q^{7} +(1338.17 - 1338.17i) q^{8} +552.618i q^{9} +O(q^{10})$	\(q+(-11.1386 - 11.1386i) q^{2} +(25.3142 + 25.3142i) q^{3} +184.138i q^{4} -151.054i q^{5} -563.931i q^{6} -332.137 q^{7} +(1338.17 - 1338.17i) q^{8} +552.618i q^{9} +(-1682.54 + 1682.54i) q^{10} +(-930.174 - 930.174i) q^{11} +(-4661.31 + 4661.31i) q^{12} -565.734i q^{13} +(3699.55 + 3699.55i) q^{14} +(3823.82 - 3823.82i) q^{15} -18026.0 q^{16} +(-2486.23 - 2486.23i) q^{17} +(6155.41 - 6155.41i) q^{18} +(-2510.14 - 2510.14i) q^{19} +27814.8 q^{20} +(-8407.80 - 8407.80i) q^{21} +20721.7i q^{22} -11240.3 q^{23} +67749.5 q^{24} -7192.43 q^{25} +(-6301.50 + 6301.50i) q^{26} +(4464.96 - 4464.96i) q^{27} -61159.1i q^{28} +(-23970.3 - 4499.53i) q^{29} -85184.3 q^{30} +(-537.894 - 537.894i) q^{31} +(115141. + 115141. i) q^{32} -47093.2i q^{33} +55386.3i q^{34} +50170.8i q^{35} -101758. q^{36} +(27533.5 - 27533.5i) q^{37} +55919.1i q^{38} +(14321.1 - 14321.1i) q^{39} +(-202137. - 202137. i) q^{40} +(82553.3 - 82553.3i) q^{41} +187303. i q^{42} +(57340.5 + 57340.5i) q^{43} +(171280. - 171280. i) q^{44} +83475.4 q^{45} +(125202. + 125202. i) q^{46} +(-106586. + 106586. i) q^{47} +(-456313. - 456313. i) q^{48} -7333.71 q^{49} +(80113.8 + 80113.8i) q^{50} -125874. i q^{51} +104173. q^{52} +107906. q^{53} -99467.1 q^{54} +(-140507. + 140507. i) q^{55} +(-444457. + 444457. i) q^{56} -127085. i q^{57} +(216878. + 317115. i) q^{58} -11827.6 q^{59} +(704111. + 704111. i) q^{60} +(-12666.7 - 12666.7i) q^{61} +11982.8i q^{62} -183545. i q^{63} -1.41137e6i q^{64} -85456.6 q^{65} +(-524554. + 524554. i) q^{66} +144718. i q^{67} +(457809. - 457809. i) q^{68} +(-284540. - 284540. i) q^{69} +(558834. - 558834. i) q^{70} +72659.2i q^{71} +(739498. + 739498. i) q^{72} +(70351.3 - 70351.3i) q^{73} -613370. q^{74} +(-182071. - 182071. i) q^{75} +(462213. - 462213. i) q^{76} +(308946. + 308946. i) q^{77} -319035. q^{78} +(135328. + 135328. i) q^{79} +2.72290e6i q^{80} +628913. q^{81} -1.83906e6 q^{82} +582524. q^{83} +(1.54819e6 - 1.54819e6i) q^{84} +(-375555. + 375555. i) q^{85} -1.27739e6i q^{86} +(-492888. - 720692. i) q^{87} -2.48947e6 q^{88} +(67243.4 + 67243.4i) q^{89} +(-929801. - 929801. i) q^{90} +187902. i q^{91} -2.06977e6i q^{92} -27232.7i q^{93} +2.37445e6 q^{94} +(-379168. + 379168. i) q^{95} +5.82943e6i q^{96} +(-699082. + 699082. i) q^{97} +(81687.4 + 81687.4i) q^{98} +(514031. - 514031. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) $ 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−11.1386	−	11.1386i	−1.39233	−	1.39233i	−0.820082	−	0.572247i	$-0.806072\pi$
$2$	−11.1386	−	11.1386i	−1.39233	−	1.39233i	−0.572247	−	0.820082i	$-0.693928\pi$
$3$	25.3142	+	25.3142i	0.937563	+	0.937563i	0.998162	−	0.0605989i	$-0.0193011\pi$
$3$	25.3142	+	25.3142i	0.937563	+	0.937563i	−0.0605989	+	0.998162i	$0.519301\pi$
$4$			184.138i			2.87716i
$5$		−	151.054i		−	1.20844i	−0.796819	−	0.604218i	$-0.793486\pi$
$5$		−	151.054i		−	1.20844i	0.796819	−	0.604218i	$-0.206514\pi$
$6$		−	563.931i		−	2.61079i
$7$	−332.137			−0.968331			−0.484165	−	0.874976i	$-0.660877\pi$
$7$	−332.137			−0.968331			−0.484165	+	0.874976i	$0.660877\pi$
$8$	1338.17	−	1338.17i	2.61362	−	2.61362i
$9$			552.618i			0.758050i
$10$	−1682.54	+	1682.54i	−1.68254	+	1.68254i
$11$	−930.174	−	930.174i	−0.698854	−	0.698854i	0.265310	−	0.964163i	$-0.414526\pi$
$11$	−930.174	−	930.174i	−0.698854	−	0.698854i	−0.964163	+	0.265310i	$0.914526\pi$
$12$	−4661.31	+	4661.31i	−2.69752	+	2.69752i
$13$		−	565.734i		−	0.257503i	−0.991677	−	0.128752i	$-0.958903\pi$
$13$		−	565.734i		−	0.257503i	0.991677	−	0.128752i	$-0.0410970\pi$
$14$	3699.55	+	3699.55i	1.34823	+	1.34823i
$15$	3823.82	−	3823.82i	1.13298	−	1.13298i
$16$	−18026.0			−4.40087
$17$	−2486.23	−	2486.23i	−0.506050	−	0.506050i	0.407261	−	0.913312i	$-0.366484\pi$
$17$	−2486.23	−	2486.23i	−0.506050	−	0.506050i	−0.913312	+	0.407261i	$0.866484\pi$
$18$	6155.41	−	6155.41i	1.05545	−	1.05545i
$19$	−2510.14	−	2510.14i	−0.365963	−	0.365963i	0.500039	−	0.866003i	$-0.333319\pi$
$19$	−2510.14	−	2510.14i	−0.365963	−	0.365963i	−0.866003	+	0.500039i	$0.833319\pi$
$20$	27814.8			3.47686
$21$	−8407.80	−	8407.80i	−0.907871	−	0.907871i
$22$			20721.7i			1.94607i
$23$	−11240.3			−0.923836			−0.461918	−	0.886923i	$-0.652839\pi$
$23$	−11240.3			−0.923836			−0.461918	+	0.886923i	$0.652839\pi$
$24$	67749.5			4.90086
$25$	−7192.43			−0.460316
$26$	−6301.50	+	6301.50i	−0.358529	+	0.358529i
$27$	4464.96	−	4464.96i	0.226844	−	0.226844i
$28$		−	61159.1i		−	2.78604i
$29$	−23970.3	−	4499.53i	−0.982834	−	0.184490i
$29$	−23970.3	−	4499.53i	−0.982834	−	0.184490i
$30$	−85184.3			−3.15497
$31$	−537.894	−	537.894i	−0.0180556	−	0.0180556i	0.698021	−	0.716077i	$-0.254064\pi$
$31$	−537.894	−	537.894i	−0.0180556	−	0.0180556i	−0.716077	+	0.698021i	$0.754064\pi$
$32$	115141.	+	115141.i	3.51384	+	3.51384i
$33$		−	47093.2i		−	1.31044i
$34$			55386.3i			1.40918i
$35$			50170.8i			1.17016i
$36$	−101758.			−2.18103
$37$	27533.5	−	27533.5i	0.543570	−	0.543570i	−0.381003	−	0.924574i	$-0.624421\pi$
$37$	27533.5	−	27533.5i	0.543570	−	0.543570i	0.924574	+	0.381003i	$0.124421\pi$
$38$			55919.1i			1.01908i
$39$	14321.1	−	14321.1i	0.241425	−	0.241425i
$40$	−202137.	−	202137.i	−3.15839	−	3.15839i
$41$	82553.3	−	82553.3i	1.19780	−	1.19780i	0.222972	−	0.974825i	$-0.428424\pi$
$41$	82553.3	−	82553.3i	1.19780	−	1.19780i	0.974825	−	0.222972i	$-0.0715757\pi$
$42$			187303.i			2.52811i
$43$	57340.5	+	57340.5i	0.721200	+	0.721200i	0.968850	−	0.247650i	$-0.0796581\pi$
$43$	57340.5	+	57340.5i	0.721200	+	0.721200i	−0.247650	+	0.968850i	$0.579658\pi$
$44$	171280.	−	171280.i	2.01071	−	2.01071i
$45$	83475.4			0.916054
$46$	125202.	+	125202.i	1.28628	+	1.28628i
$47$	−106586.	+	106586.i	−1.02661	+	1.02661i	−0.0269789	+	0.999636i	$0.508589\pi$
$47$	−106586.	+	106586.i	−1.02661	+	1.02661i	−0.999636	+	0.0269789i	$0.991411\pi$
$48$	−456313.	−	456313.i	−4.12609	−	4.12609i
$49$	−7333.71			−0.0623355
$50$	80113.8	+	80113.8i	0.640910	+	0.640910i
$51$		−	125874.i		−	0.948909i
$52$	104173.			0.740876
$53$	107906.			0.724799			0.362400	−	0.932023i	$-0.381958\pi$
$53$	107906.			0.724799			0.362400	+	0.932023i	$0.381958\pi$
$54$	−99467.1			−0.631682
$55$	−140507.	+	140507.i	−0.844519	+	0.844519i
$56$	−444457.	+	444457.i	−2.53085	+	2.53085i
$57$		−	127085.i		−	0.686228i
$58$	216878.	+	317115.i	1.11156	+	1.62530i
$59$	−11827.6			−0.0575890			−0.0287945	−	0.999585i	$-0.509167\pi$
$59$	−11827.6			−0.0575890			−0.0287945	+	0.999585i	$0.509167\pi$
$60$	704111.	+	704111.i	3.25977	+	3.25977i
$61$	−12666.7	−	12666.7i	−0.0558050	−	0.0558050i	0.678654	−	0.734459i	$-0.262564\pi$
$61$	−12666.7	−	12666.7i	−0.0558050	−	0.0558050i	−0.734459	+	0.678654i	$0.762564\pi$
$62$			11982.8i			0.0502786i
$63$		−	183545.i		−	0.734043i
$64$		−	1.41137e6i		−	5.38396i
$65$	−85456.6			−0.311176
$66$	−524554.	+	524554.i	−1.82456	+	1.82456i
$67$			144718.i			0.481170i	0.970628	+	0.240585i	$0.0773393\pi$
$67$			144718.i			0.481170i	−0.970628	+	0.240585i	$0.922661\pi$
$68$	457809.	−	457809.i	1.45599	−	1.45599i
$69$	−284540.	−	284540.i	−0.866154	−	0.866154i
$70$	558834.	−	558834.i	1.62925	−	1.62925i
$71$			72659.2i			0.203009i	0.994835	+	0.101505i	$0.0323657\pi$
$71$			72659.2i			0.203009i	−0.994835	+	0.101505i	$0.967634\pi$
$72$	739498.	+	739498.i	1.98125	+	1.98125i
$73$	70351.3	−	70351.3i	0.180844	−	0.180844i	−0.610880	−	0.791723i	$-0.709184\pi$
$73$	70351.3	−	70351.3i	0.180844	−	0.180844i	0.791723	+	0.610880i	$0.209184\pi$
$74$	−613370.			−1.51366
$75$	−182071.	−	182071.i	−0.431575	−	0.431575i
$76$	462213.	−	462213.i	1.05293	−	1.05293i
$77$	308946.	+	308946.i	0.676721	+	0.676721i
$78$	−319035.			−0.672287
$79$	135328.	+	135328.i	0.274477	+	0.274477i	0.830899	−	0.556423i	$-0.187826\pi$
$79$	135328.	+	135328.i	0.274477	+	0.274477i	−0.556423	+	0.830899i	$0.687826\pi$
$80$			2.72290e6i			5.31816i
$81$	628913.			1.18341
$82$	−1.83906e6			−3.33545
$83$	582524.			1.01878			0.509389	−	0.860536i	$-0.329871\pi$
$83$	582524.			1.01878			0.509389	+	0.860536i	$0.329871\pi$
$84$	1.54819e6	−	1.54819e6i	2.61209	−	2.61209i
$85$	−375555.	+	375555.i	−0.611529	+	0.611529i
$86$		−	1.27739e6i		−	2.00829i
$87$	−492888.	−	720692.i	−0.748498	−	1.09444i
$88$	−2.48947e6			−3.65307
$89$	67243.4	+	67243.4i	0.0953848	+	0.0953848i	0.753189	−	0.657804i	$-0.228515\pi$
$89$	67243.4	+	67243.4i	0.0953848	+	0.0953848i	−0.657804	+	0.753189i	$0.728515\pi$
$90$	−929801.	−	929801.i	−1.27545	−	1.27545i
$91$			187902.i			0.249348i
$92$		−	2.06977e6i		−	2.65802i
$93$		−	27232.7i		−	0.0338565i
$94$	2.37445e6			2.85877
$95$	−379168.	+	379168.i	−0.442243	+	0.442243i
$96$			5.82943e6i			6.58889i
$97$	−699082.	+	699082.i	−0.765972	+	0.765972i	−0.977395	−	0.211422i	$-0.932190\pi$
$97$	−699082.	+	699082.i	−0.765972	+	0.765972i	0.211422	+	0.977395i	$0.432190\pi$
$98$	81687.4	+	81687.4i	0.0867914	+	0.0867914i
$99$	514031.	−	514031.i	0.529766	−	0.529766i
$100$		−	1.32440e6i		−	1.32440i
$101$	−426229.	−	426229.i	−0.413693	−	0.413693i	0.469330	−	0.883023i	$-0.344496\pi$
$101$	−426229.	−	426229.i	−0.413693	−	0.413693i	−0.883023	+	0.469330i	$0.844496\pi$
$102$	−1.40206e6	+	1.40206e6i	−1.32119	+	1.32119i
$103$	−1.36702e6			−1.25101			−0.625506	−	0.780219i	$-0.715108\pi$
$103$	−1.36702e6			−1.25101			−0.625506	+	0.780219i	$0.715108\pi$
$104$	−757050.	−	757050.i	−0.673014	−	0.673014i
$105$	−1.27003e6	+	1.27003e6i	−1.09710	+	1.09710i
$106$	−1.20192e6	−	1.20192e6i	−1.00916	−	1.00916i
$107$	484858.			0.395788			0.197894	−	0.980223i	$-0.436590\pi$
$107$	484858.			0.395788			0.197894	+	0.980223i	$0.436590\pi$
$108$	822169.	+	822169.i	0.652664	+	0.652664i
$109$		−	2.30070e6i		−	1.77656i	−0.459300	−	0.888281i	$-0.651900\pi$
$109$		−	2.30070e6i		−	1.77656i	0.459300	−	0.888281i	$-0.348100\pi$
$110$	3.13011e6			2.35170
$111$	1.39398e6			1.01926
$112$	5.98710e6			4.26150
$113$	−1.21804e6	+	1.21804e6i	−0.844162	+	0.844162i	−0.989397	−	0.145235i	$-0.953606\pi$
$113$	−1.21804e6	+	1.21804e6i	−0.844162	+	0.844162i	0.145235	+	0.989397i	$0.453606\pi$
$114$	−1.41555e6	+	1.41555e6i	−0.955454	+	0.955454i
$115$			1.69790e6i			1.11640i
$116$	828534.	−	4.41385e6i	0.530807	−	2.82777i
$117$	312635.			0.195200
$118$	131743.	+	131743.i	0.0801828	+	0.0801828i
$119$	825769.	+	825769.i	0.490024	+	0.490024i
$120$		−	1.02339e7i		−	5.92237i
$121$		−	41113.0i		−	0.0232072i
$122$			282179.i			0.155398i
$123$	4.17954e6			2.24602
$124$	99046.6	−	99046.6i	0.0519487	−	0.0519487i
$125$		−	1.27378e6i		−	0.652174i
$126$	−2.04444e6	+	2.04444e6i	−1.02203	+	1.02203i
$127$	−242843.	−	242843.i	−0.118554	−	0.118554i	0.645341	−	0.763895i	$-0.276715\pi$
$127$	−242843.	−	242843.i	−0.118554	−	0.118554i	−0.763895	+	0.645341i	$0.776715\pi$
$128$	−8.35170e6	+	8.35170e6i	−3.98240	+	3.98240i
$129$			2.90306e6i			1.35234i
$130$	951870.	+	951870.i	0.433259	+	0.433259i
$131$	−8487.24	+	8487.24i	−0.00377531	+	0.00377531i	−0.708992	−	0.705217i	$-0.750850\pi$
$131$	−8487.24	+	8487.24i	−0.00377531	+	0.00377531i	0.705217	+	0.708992i	$0.250850\pi$
$132$	8.67165e6			3.77034
$133$	833712.	+	833712.i	0.354374	+	0.354374i
$134$	1.61196e6	−	1.61196e6i	0.669946	−	0.669946i
$135$	−674452.	−	674452.i	−0.274126	−	0.274126i
$136$	−6.65399e6			−2.64524
$137$	−360196.	−	360196.i	−0.140080	−	0.140080i	0.633589	−	0.773670i	$-0.281581\pi$
$137$	−360196.	−	360196.i	−0.140080	−	0.140080i	−0.773670	+	0.633589i	$0.781581\pi$
$138$			6.33876e6i			2.41194i
$139$	4.53780e6			1.68967			0.844833	−	0.535030i	$-0.179700\pi$
$139$	4.53780e6			1.68967			0.844833	+	0.535030i	$0.179700\pi$
$140$	−9.23835e6			−3.36675
$141$	−5.39629e6			−1.92503
$142$	809324.	−	809324.i	0.282656	−	0.282656i
$143$	−526231.	+	526231.i	−0.179957	+	0.179957i
$144$		−	9.96147e6i		−	3.33608i
$145$	−679673.	+	3.62083e6i	−0.222944	+	1.18769i
$146$	−1.56723e6			−0.503587
$147$	−185647.	−	185647.i	−0.0584434	−	0.0584434i
$148$	5.06996e6	+	5.06996e6i	1.56394	+	1.56394i
$149$		−	3.95804e6i		−	1.19652i	−0.801301	−	0.598262i	$-0.795858\pi$
$149$		−	3.95804e6i		−	1.19652i	0.801301	−	0.598262i	$-0.204142\pi$
$150$			4.05603e6i			1.20179i
$151$			80452.7i			0.0233674i	0.999932	+	0.0116837i	$0.00371912\pi$
$151$			80452.7i			0.0233674i	−0.999932	+	0.0116837i	$0.996281\pi$
$152$	−6.71800e6			−1.91298
$153$	1.37393e6	−	1.37393e6i	0.383611	−	0.383611i
$154$		−	6.88246e6i		−	1.88444i
$155$	−81251.2	+	81251.2i	−0.0218190	+	0.0218190i
$156$	2.63706e6	+	2.63706e6i	0.694619	+	0.694619i
$157$	−2.60952e6	+	2.60952e6i	−0.674314	+	0.674314i	−0.958708	−	0.284394i	$-0.908208\pi$
$157$	−2.60952e6	+	2.60952e6i	−0.674314	+	0.674314i	0.284394	+	0.958708i	$0.408208\pi$
$158$		−	3.01473e6i		−	0.764324i
$159$	2.73155e6	+	2.73155e6i	0.679545	+	0.679545i
$160$	1.73926e7	−	1.73926e7i	4.24624	−	4.24624i
$161$	3.73333e6			0.894579
$162$	−7.00522e6	−	7.00522e6i	−1.64770	−	1.64770i
$163$	−746595.	+	746595.i	−0.172394	+	0.172394i	−0.788030	−	0.615636i	$-0.788899\pi$
$163$	−746595.	+	746595.i	−0.172394	+	0.172394i	0.615636	+	0.788030i	$0.288899\pi$
$164$	1.52012e7	+	1.52012e7i	3.44625	+	3.44625i
$165$	−7.11364e6			−1.58358
$166$	−6.48852e6	−	6.48852e6i	−1.41847	−	1.41847i
$167$		−	9.10378e6i		−	1.95466i	−0.211712	−	0.977332i	$-0.567904\pi$
$167$		−	9.10378e6i		−	1.95466i	0.211712	−	0.977332i	$-0.432096\pi$
$168$	−2.25022e7			−4.74566
$169$	4.50675e6			0.933692
$170$	8.36634e6			1.70290
$171$	1.38715e6	−	1.38715e6i	0.277418	−	0.277418i
$172$	−1.05586e7	+	1.05586e7i	−2.07501	+	2.07501i
$173$		−	2.33769e6i		−	0.451490i	−0.974186	−	0.225745i	$-0.927518\pi$
$173$		−	2.33769e6i		−	0.451490i	0.974186	−	0.225745i	$-0.0724817\pi$
$174$	−2.53742e6	+	1.35176e7i	−0.481665	+	2.56598i
$175$	2.38888e6			0.445738
$176$	1.67673e7	+	1.67673e7i	3.07556	+	3.07556i
$177$	−299406.	−	299406.i	−0.0539934	−	0.0539934i
$178$		−	1.49800e6i		−	0.265614i
$179$		−	9.94618e6i		−	1.73419i	−0.498141	−	0.867096i	$-0.665984\pi$
$179$		−	9.94618e6i		−	1.73419i	0.498141	−	0.867096i	$-0.334016\pi$
$180$			1.53710e7i			2.63563i
$181$	273079.			0.0460525			0.0230262	−	0.999735i	$-0.492670\pi$
$181$	273079.			0.0460525			0.0230262	+	0.999735i	$0.492670\pi$
$182$	2.09296e6	−	2.09296e6i	0.347174	−	0.347174i
$183$		−	641293.i		−	0.104641i
$184$	−1.50415e7	+	1.50415e7i	−2.41455	+	2.41455i
$185$	−4.15905e6	−	4.15905e6i	−0.656869	−	0.656869i
$186$	−303335.	+	303335.i	−0.0471393	+	0.0471393i
$187$			4.62525e6i			0.707310i
$188$	−1.96266e7	−	1.96266e7i	−2.95373	−	2.95373i
$189$	−1.48298e6	+	1.48298e6i	−0.219660	+	0.219660i
$190$	8.44682e6			1.23149
$191$	7.20196e6	+	7.20196e6i	1.03360	+	1.03360i	0.999416	+	0.0341798i	$0.0108819\pi$
$191$	7.20196e6	+	7.20196e6i	1.03360	+	1.03360i	0.0341798	+	0.999416i	$0.489118\pi$
$192$	3.57278e7	−	3.57278e7i	5.04780	−	5.04780i
$193$	−6.43714e6	−	6.43714e6i	−0.895409	−	0.895409i	0.0996172	−	0.995026i	$-0.468238\pi$
$193$	−6.43714e6	−	6.43714e6i	−0.895409	−	0.895409i	−0.995026	+	0.0996172i	$0.968238\pi$
$194$	1.55736e7			2.13297
$195$	−2.16327e6	−	2.16327e6i	−0.291747	−	0.291747i
$196$		−	1.35041e6i		−	0.179349i
$197$	−5.60144e6			−0.732658			−0.366329	−	0.930485i	$-0.619386\pi$
$197$	−5.60144e6			−0.732658			−0.366329	+	0.930485i	$0.619386\pi$
$198$	−1.14512e7			−1.47522
$199$	−9.70627e6			−1.23167			−0.615833	−	0.787877i	$-0.711180\pi$
$199$	−9.70627e6			−1.23167			−0.615833	+	0.787877i	$0.711180\pi$
$200$	−9.62471e6	+	9.62471e6i	−1.20309	+	1.20309i
$201$	−3.66342e6	+	3.66342e6i	−0.451127	+	0.451127i
$202$			9.49520e6i			1.15199i
$203$	7.96145e6	+	1.49446e6i	0.951709	+	0.178647i
$204$	2.31781e7			2.73016
$205$	−1.24700e7	−	1.24700e7i	−1.44746	−	1.44746i
$206$	1.52267e7	+	1.52267e7i	1.74182	+	1.74182i
$207$		−	6.21160e6i		−	0.700313i
$208$			1.01979e7i			1.13324i
$209$			4.66974e6i			0.511510i
$210$	2.82929e7			3.05506
$211$	3.93433e6	−	3.93433e6i	0.418816	−	0.418816i	−0.465980	−	0.884795i	$-0.654298\pi$
$211$	3.93433e6	−	3.93433e6i	0.418816	−	0.418816i	0.884795	+	0.465980i	$0.154298\pi$
$212$			1.98696e7i			2.08536i
$213$	−1.83931e6	+	1.83931e6i	−0.190334	+	0.190334i
$214$	−5.40065e6	−	5.40065e6i	−0.551067	−	0.551067i
$215$	8.66153e6	−	8.66153e6i	0.871524	−	0.871524i
$216$		−	1.19498e7i		−	1.18576i
$217$	178655.	+	178655.i	0.0174838	+	0.0174838i
$218$	−2.56266e7	+	2.56266e7i	−2.47356	+	2.47356i
$219$	3.56177e6			0.339105
$220$	−2.58727e7	−	2.58727e7i	−2.42981	−	2.42981i
$221$	−1.40654e6	+	1.40654e6i	−0.130310	+	0.130310i
$222$	−1.55270e7	−	1.55270e7i	−1.41915	−	1.41915i
$223$	−819363.			−0.0738859			−0.0369430	−	0.999317i	$-0.511762\pi$
$223$	−819363.			−0.0738859			−0.0369430	+	0.999317i	$0.511762\pi$
$224$	−3.82428e7	−	3.82428e7i	−3.40256	−	3.40256i
$225$		−	3.97467e6i		−	0.348942i
$226$	2.71346e7			2.35070
$227$	−1.54861e7			−1.32393			−0.661963	−	0.749537i	$-0.730276\pi$
$227$	−1.54861e7			−1.32393			−0.661963	+	0.749537i	$0.730276\pi$
$228$	2.34011e7			1.97438
$229$	−2.52400e6	+	2.52400e6i	−0.210176	+	0.210176i	−0.804342	−	0.594166i	$-0.797482\pi$
$229$	−2.52400e6	+	2.52400e6i	−0.210176	+	0.210176i	0.594166	+	0.804342i	$0.297482\pi$
$230$	1.89123e7	−	1.89123e7i	1.55439	−	1.55439i
$231$			1.56414e7i			1.26894i
$232$	−3.80976e7	+	2.60553e7i	−3.05094	+	2.08657i
$233$	2.36716e7			1.87137			0.935684	−	0.352839i	$-0.114784\pi$
$233$	2.36716e7			1.87137			0.935684	+	0.352839i	$0.114784\pi$
$234$	−3.48233e6	−	3.48233e6i	−0.271783	−	0.271783i
$235$	1.61003e7	+	1.61003e7i	1.24060	+	1.24060i
$236$		−	2.17791e6i		−	0.165693i
$237$			6.85143e6i			0.514679i
$238$		−	1.83959e7i		−	1.36455i
$239$	1.12358e7			0.823022			0.411511	−	0.911405i	$-0.365001\pi$
$239$	1.12358e7			0.823022			0.411511	+	0.911405i	$0.365001\pi$
$240$	−6.89281e7	+	6.89281e7i	−4.98612	+	4.98612i
$241$			1.66096e7i			1.18661i	0.804978	+	0.593305i	$0.202177\pi$
$241$			1.66096e7i			1.18661i	−0.804978	+	0.593305i	$0.797823\pi$
$242$	−457942.	+	457942.i	−0.0323120	+	0.0323120i
$243$	1.26655e7	+	1.26655e7i	0.882678	+	0.882678i
$244$	2.33241e6	−	2.33241e6i	0.160560	−	0.160560i
$245$			1.10779e6i			0.0753284i
$246$	−4.65544e7	−	4.65544e7i	−3.12720	−	3.12720i
$247$	−1.42007e6	+	1.42007e6i	−0.0942367	+	0.0942367i
$248$	−1.43959e6			−0.0943807
$249$	1.47461e7	+	1.47461e7i	0.955169	+	0.955169i
$250$	−1.41881e7	+	1.41881e7i	−0.908040	+	0.908040i
$251$	−3.65582e6	−	3.65582e6i	−0.231187	−	0.231187i	0.582001	−	0.813188i	$-0.302270\pi$
$251$	−3.65582e6	−	3.65582e6i	−0.231187	−	0.231187i	−0.813188	+	0.582001i	$0.802270\pi$
$252$	3.37976e7			2.11196
$253$	1.04554e7	+	1.04554e7i	0.645626	+	0.645626i
$254$			5.40988e6i			0.330131i
$255$	−1.90138e7			−1.14669
$256$	9.57251e7			5.70566
$257$	4.10136e6			0.241618			0.120809	−	0.992676i	$-0.461451\pi$
$257$	4.10136e6			0.241618			0.120809	+	0.992676i	$0.461451\pi$
$258$	3.23361e7	−	3.23361e7i	1.88290	−	1.88290i
$259$	−9.14489e6	+	9.14489e6i	−0.526356	+	0.526356i
$260$		−	1.57358e7i		−	0.895301i
$261$	2.48652e6	−	1.32465e7i	0.139853	−	0.745037i
$262$	189072.			0.0105129
$263$	6.98649e6	+	6.98649e6i	0.384054	+	0.384054i	0.872560	−	0.488507i	$-0.162458\pi$
$263$	6.98649e6	+	6.98649e6i	0.384054	+	0.384054i	−0.488507	+	0.872560i	$0.662458\pi$
$264$	−6.30189e7	−	6.30189e7i	−3.42499	−	3.42499i
$265$		−	1.62997e7i		−	0.875873i
$266$		−	1.85728e7i		−	0.986809i
$267$			3.40442e6i			0.178859i
$268$	−2.66481e7			−1.38440
$269$	1.69226e7	−	1.69226e7i	0.869383	−	0.869383i	−0.123021	−	0.992404i	$-0.539258\pi$
$269$	1.69226e7	−	1.69226e7i	0.869383	−	0.869383i	0.992404	+	0.123021i	$0.0392582\pi$
$270$			1.50249e7i			0.763346i
$271$	9.50817e6	−	9.50817e6i	0.477737	−	0.477737i	−0.426670	−	0.904407i	$-0.640313\pi$
$271$	9.50817e6	−	9.50817e6i	0.477737	−	0.477737i	0.904407	+	0.426670i	$0.140313\pi$
$272$	4.48166e7	+	4.48166e7i	2.22706	+	2.22706i
$273$	−4.75658e6	+	4.75658e6i	−0.233780	+	0.233780i
$274$			8.02417e6i			0.390075i
$275$	6.69021e6	+	6.69021e6i	0.321693	+	0.321693i
$276$	5.23945e7	−	5.23945e7i	2.49206	−	2.49206i
$277$	−9.18795e6			−0.432294			−0.216147	−	0.976361i	$-0.569349\pi$
$277$	−9.18795e6			−0.432294			−0.216147	+	0.976361i	$0.569349\pi$
$278$	−5.05449e7	−	5.05449e7i	−2.35257	−	2.35257i
$279$	297250.	−	297250.i	0.0136870	−	0.0136870i
$280$	6.71372e7	+	6.71372e7i	3.05836	+	3.05836i
$281$	−4.19053e7			−1.88864			−0.944322	−	0.329023i	$-0.893280\pi$
$281$	−4.19053e7			−1.88864			−0.944322	+	0.329023i	$0.893280\pi$
$282$	6.01073e7	+	6.01073e7i	2.68028	+	2.68028i
$283$		−	1.11940e7i		−	0.493886i	−0.969030	−	0.246943i	$-0.920574\pi$
$283$		−	1.11940e7i		−	0.493886i	0.969030	−	0.246943i	$-0.0794260\pi$
$284$	−1.33793e7			−0.584089
$285$	−1.91967e7			−0.829262
$286$	1.17230e7			0.501118
$287$	−2.74191e7	+	2.74191e7i	−1.15986	+	1.15986i
$288$	−6.36292e7	+	6.36292e7i	−2.66366	+	2.66366i
$289$		−	1.17749e7i		−	0.487826i
$290$	4.79017e7	−	3.27604e7i	1.96407	−	1.34324i
$291$	−3.53934e7			−1.43630
$292$	1.29543e7	+	1.29543e7i	0.520315	+	0.520315i
$293$	1.36957e7	+	1.36957e7i	0.544479	+	0.544479i	0.924839	−	0.380360i	$-0.124200\pi$
$293$	1.36957e7	+	1.36957e7i	0.544479	+	0.544479i	−0.380360	+	0.924839i	$0.624200\pi$
$294$			4.13570e6i			0.162745i
$295$			1.78661e6i			0.0695926i
$296$		−	7.36890e7i		−	2.84137i
$297$	−8.30639e6			−0.317061
$298$	−4.40871e7	+	4.40871e7i	−1.66595	+	1.66595i
$299$			6.35903e6i			0.237891i
$300$	3.35261e7	−	3.35261e7i	1.24171	−	1.24171i
$301$	−1.90449e7	−	1.90449e7i	−0.698360	−	0.698360i
$302$	896133.	−	896133.i	0.0325351	−	0.0325351i
$303$		−	2.15793e7i		−	0.775727i
$304$	4.52477e7	+	4.52477e7i	1.61056	+	1.61056i
$305$	−1.91336e6	+	1.91336e6i	−0.0674367	+	0.0674367i
$306$	−3.06075e7			−1.06823
$307$	2.52919e7	+	2.52919e7i	0.874110	+	0.874110i	0.992917	−	0.118807i	$-0.0379071\pi$
$307$	2.52919e7	+	2.52919e7i	0.874110	+	0.874110i	−0.118807	+	0.992917i	$0.537907\pi$
$308$	−5.68886e7	+	5.68886e7i	−1.94703	+	1.94703i
$309$	−3.46049e7	−	3.46049e7i	−1.17290	−	1.17290i
$310$	1.81005e6			0.0607584
$311$	−2.74479e7	−	2.74479e7i	−0.912489	−	0.912489i	0.0839790	−	0.996468i	$-0.473237\pi$
$311$	−2.74479e7	−	2.74479e7i	−0.912489	−	0.912489i	−0.996468	+	0.0839790i	$0.973237\pi$
$312$		−	3.83282e7i		−	1.26199i
$313$	3.52404e7			1.14923			0.574617	−	0.818423i	$-0.305151\pi$
$313$	3.52404e7			1.14923			0.574617	+	0.818423i	$0.305151\pi$
$314$	5.81330e7			1.87773
$315$	−2.77253e7			−0.887043
$316$	−2.49190e7	+	2.49190e7i	−0.789713	+	0.789713i
$317$	1.80032e7	−	1.80032e7i	0.565160	−	0.565160i	−0.365609	−	0.930769i	$-0.619139\pi$
$317$	1.80032e7	−	1.80032e7i	0.565160	−	0.565160i	0.930769	+	0.365609i	$0.119139\pi$
$318$		−	6.08515e7i		−	1.89230i
$319$	1.81113e7	+	2.64819e7i	0.557926	+	0.815789i
$320$	−2.13194e8			−6.50617
$321$	1.22738e7	+	1.22738e7i	0.371077	+	0.371077i
$322$	−4.15841e7	−	4.15841e7i	−1.24555	−	1.24555i
$323$			1.24816e7i			0.370392i
$324$			1.15807e8i			3.40486i
$325$			4.06900e6i			0.118533i
$326$	1.66321e7			0.480058
$327$	5.82404e7	−	5.82404e7i	1.66564	−	1.66564i
$328$		−	2.20941e8i		−	6.26116i
$329$	3.54013e7	−	3.54013e7i	0.994103	−	0.994103i
$330$	7.92362e7	+	7.92362e7i	2.20486	+	2.20486i
$331$	3.63550e7	−	3.63550e7i	1.00249	−	1.00249i	0.00249430	−	0.999997i	$-0.499206\pi$
$331$	3.63550e7	−	3.63550e7i	1.00249	−	1.00249i	0.999997	−	0.00249430i	$-0.000793961\pi$
$332$			1.07265e8i			2.93118i
$333$	1.52155e7	+	1.52155e7i	0.412053	+	0.412053i
$334$	−1.01404e8	+	1.01404e8i	−2.72153	+	2.72153i
$335$	2.18603e7			0.581463
$336$	1.51559e8	+	1.51559e8i	3.99542	+	3.99542i
$337$	−1.81622e7	+	1.81622e7i	−0.474546	+	0.474546i	−0.903382	−	0.428837i	$-0.858924\pi$
$337$	−1.81622e7	+	1.81622e7i	−0.474546	+	0.474546i	0.428837	+	0.903382i	$0.358924\pi$
$338$	−5.01990e7	−	5.01990e7i	−1.30001	−	1.30001i
$339$	−6.16674e7			−1.58291
$340$	−6.91540e7	−	6.91540e7i	−1.75946	−	1.75946i
$341$			1.00067e6i			0.0252364i
$342$	−3.09019e7			−0.772515
$343$	4.15114e7			1.02869
$344$	1.53463e8			3.76988
$345$	−4.29809e7	+	4.29809e7i	−1.04669	+	1.04669i
$346$	−2.60387e7	+	2.60387e7i	−0.628623	+	0.628623i
$347$		−	2.98775e7i		−	0.715083i	−0.933897	−	0.357542i	$-0.883615\pi$
$347$		−	2.98775e7i		−	0.715083i	0.933897	−	0.357542i	$-0.116385\pi$
$348$	1.32707e8	−	9.07595e7i	3.14888	−	2.15355i
$349$	−2.97620e7			−0.700142			−0.350071	−	0.936723i	$-0.613843\pi$
$349$	−2.97620e7			−0.700142			−0.350071	+	0.936723i	$0.613843\pi$
$350$	−2.66088e7	−	2.66088e7i	−0.620613	−	0.620613i
$351$	−2.52598e6	−	2.52598e6i	−0.0584129	−	0.0584129i
$352$		−	2.14203e8i		−	4.91132i
$353$			6.12168e7i			1.39170i	0.718186	+	0.695851i	$0.244973\pi$
$353$			6.12168e7i			1.39170i	−0.718186	+	0.695851i	$0.755027\pi$
$354$			6.66994e6i			0.150353i
$355$	1.09755e7			0.245324
$356$	−1.23821e7	+	1.23821e7i	−0.274437	+	0.274437i
$357$			4.18074e7i			0.918857i
$358$	−1.10787e8	+	1.10787e8i	−2.41456	+	2.41456i
$359$	−4.62426e7	−	4.62426e7i	−0.999444	−	0.999444i	0.000555557	−	1.00000i	$-0.499823\pi$
$359$	−4.62426e7	−	4.62426e7i	−0.999444	−	0.999444i	−1.00000		0.000555557i	$0.999823\pi$
$360$	1.11704e8	−	1.11704e8i	2.39421	−	2.39421i
$361$		−	3.44442e7i		−	0.732142i
$362$	−3.04173e6	−	3.04173e6i	−0.0641202	−	0.0641202i
$363$	1.04074e6	−	1.04074e6i	0.0217582	−	0.0217582i
$364$	−3.45998e7			−0.717413
$365$	−1.06269e7	−	1.06269e7i	−0.218538	−	0.218538i
$366$	−7.14313e6	+	7.14313e6i	−0.145695	+	0.145695i
$367$	2.38093e7	+	2.38093e7i	0.481669	+	0.481669i	0.905664	−	0.423996i	$-0.139373\pi$
$367$	2.38093e7	+	2.38093e7i	0.481669	+	0.481669i	−0.423996	+	0.905664i	$0.639373\pi$
$368$	2.02617e8			4.06568
$369$	4.56205e7	+	4.56205e7i	0.907989	+	0.907989i
$370$			9.26522e7i			1.82916i
$371$	−3.58396e7			−0.701846
$372$	5.01457e6			0.0974104
$373$	−1.46052e7			−0.281437			−0.140719	−	0.990050i	$-0.544941\pi$
$373$	−1.46052e7			−0.281437			−0.140719	+	0.990050i	$0.544941\pi$
$374$	5.15189e7	−	5.15189e7i	0.984808	−	0.984808i
$375$	3.22446e7	−	3.22446e7i	0.611454	−	0.611454i
$376$			2.85261e8i			5.36636i
$377$	−2.54554e6	+	1.35608e7i	−0.0475068	+	0.253083i
$378$	3.30368e7			0.611677
$379$	9.95358e6	+	9.95358e6i	0.182836	+	0.182836i	0.792590	−	0.609754i	$-0.208732\pi$
$379$	9.95358e6	+	9.95358e6i	0.182836	+	0.182836i	−0.609754	+	0.792590i	$0.708732\pi$
$380$	−6.98192e7	−	6.98192e7i	−1.27240	−	1.27240i
$381$		−	1.22948e7i		−	0.222303i
$382$		−	1.60440e8i		−	2.87821i
$383$			4.19074e6i			0.0745923i	0.999304	+	0.0372962i	$0.0118745\pi$
$383$			4.19074e6i			0.0745923i	−0.999304	+	0.0372962i	$0.988126\pi$
$384$	−4.22833e8			−7.46751
$385$	4.66676e7	−	4.66676e7i	0.817774	−	0.817774i
$386$			1.43402e8i			2.49341i
$387$	−3.16874e7	+	3.16874e7i	−0.546706	+	0.546706i
$388$	−1.28728e8	−	1.28728e8i	−2.20382	−	2.20382i
$389$	−5.54611e7	+	5.54611e7i	−0.942192	+	0.942192i	−0.998418	−	0.0562263i	$-0.982093\pi$
$389$	−5.54611e7	+	5.54611e7i	−0.942192	+	0.942192i	0.0562263	+	0.998418i	$0.482093\pi$
$390$			4.81917e7i			0.812415i
$391$	2.79459e7	+	2.79459e7i	0.467507	+	0.467507i
$392$	−9.81376e6	+	9.81376e6i	−0.162921	+	0.162921i
$393$	−429695.			−0.00707918
$394$	6.23924e7	+	6.23924e7i	1.02010	+	1.02010i
$395$	2.04419e7	−	2.04419e7i	0.331687	−	0.331687i
$396$	9.46527e7	+	9.46527e7i	1.52422	+	1.52422i
$397$	6.57336e7			1.05055			0.525274	−	0.850933i	$-0.323963\pi$
$397$	6.57336e7			1.05055			0.525274	+	0.850933i	$0.323963\pi$
$398$	1.08114e8	+	1.08114e8i	1.71488	+	1.71488i
$399$			4.22095e7i			0.664495i
$400$	1.29650e8			2.02579
$401$	8.81817e7			1.36756			0.683778	−	0.729690i	$-0.260336\pi$
$401$	8.81817e7			1.36756			0.683778	+	0.729690i	$0.260336\pi$
$402$	8.16110e7			1.25623
$403$	−304305.	+	304305.i	−0.00464937	+	0.00464937i
$404$	7.84849e7	−	7.84849e7i	1.19026	−	1.19026i
$405$		−	9.50000e7i		−	1.43007i
$406$	−7.20334e7	−	1.05326e8i	−1.07636	−	1.57383i
$407$	−5.12218e7			−0.759752
$408$	−1.68441e8	−	1.68441e8i	−2.48008	−	2.48008i
$409$	−2.15291e7	−	2.15291e7i	−0.314671	−	0.314671i	0.532045	−	0.846716i	$-0.321424\pi$
$409$	−2.15291e7	−	2.15291e7i	−0.314671	−	0.314671i	−0.846716	+	0.532045i	$0.821424\pi$
$410$			2.77798e8i			4.03068i
$411$		−	1.82361e7i		−	0.262668i
$412$		−	2.51719e8i		−	3.59936i
$413$	3.92838e6			0.0557652
$414$	−6.91887e7	+	6.91887e7i	−0.975066	+	0.975066i
$415$		−	8.79928e7i		−	1.23113i
$416$	6.51394e7	−	6.51394e7i	0.904824	−	0.904824i
$417$	1.14871e8	+	1.14871e8i	1.58417	+	1.58417i
$418$	5.20145e7	−	5.20145e7i	0.712189	−	0.712189i
$419$		−	6.62264e7i		−	0.900303i	−0.892952	−	0.450152i	$-0.851370\pi$
$419$		−	6.62264e7i		−	0.900303i	0.892952	−	0.450152i	$-0.148630\pi$
$420$	−2.33862e8	−	2.33862e8i	−3.15654	−	3.15654i
$421$	6.76314e7	−	6.76314e7i	0.906363	−	0.906363i	−0.0896137	−	0.995977i	$-0.528563\pi$
$421$	6.76314e7	−	6.76314e7i	0.906363	−	0.906363i	0.995977	+	0.0896137i	$0.0285632\pi$
$422$	−8.76460e7			−1.16626
$423$	−5.89015e7	−	5.89015e7i	−0.778225	−	0.778225i
$424$	1.44397e8	−	1.44397e8i	1.89435	−	1.89435i
$425$	1.78820e7	+	1.78820e7i	0.232943	+	0.232943i
$426$	4.09748e7			0.530015
$427$	4.20707e6	+	4.20707e6i	0.0540377	+	0.0540377i
$428$			8.92807e7i			1.13874i
$429$	−2.66423e7			−0.337442
$430$	−1.92955e8			−2.42689
$431$	−1.58374e8			−1.97811			−0.989057	−	0.147537i	$-0.952865\pi$
$431$	−1.58374e8			−1.97811			−0.989057	+	0.147537i	$0.952865\pi$
$432$	−8.04852e7	+	8.04852e7i	−0.998309	+	0.998309i
$433$	−2.27896e7	+	2.27896e7i	−0.280720	+	0.280720i	−0.833396	−	0.552676i	$-0.813607\pi$
$433$	−2.27896e7	+	2.27896e7i	−0.280720	+	0.280720i	0.552676	+	0.833396i	$0.313607\pi$
$434$		−	3.97993e6i		−	0.0486863i
$435$	−1.08864e8	+	7.44530e7i	−1.32256	+	0.904512i
$436$	4.23646e8			5.11145
$437$	2.82148e7	+	2.82148e7i	0.338090	+	0.338090i
$438$	−3.96733e7	−	3.96733e7i	−0.472145	−	0.472145i
$439$			8.72394e7i			1.03114i	0.856846	+	0.515572i	$0.172420\pi$
$439$			8.72394e7i			1.03114i	−0.856846	+	0.515572i	$0.827580\pi$
$440$			3.76045e8i			4.41450i
$441$		−	4.05274e6i		−	0.0472534i
$442$	3.13339e7			0.362867
$443$	−5.49263e7	+	5.49263e7i	−0.631785	+	0.631785i	−0.948515	−	0.316731i	$-0.897415\pi$
$443$	−5.49263e7	+	5.49263e7i	−0.631785	+	0.631785i	0.316731	+	0.948515i	$0.397415\pi$
$444$			2.56684e8i			2.93258i
$445$	1.01574e7	−	1.01574e7i	0.115266	−	0.115266i
$446$	9.12658e6	+	9.12658e6i	0.102873	+	0.102873i
$447$	1.00195e8	−	1.00195e8i	1.12182	−	1.12182i
$448$			4.68770e8i			5.21345i
$449$	−7.78946e7	−	7.78946e7i	−0.860535	−	0.860535i	0.130865	−	0.991400i	$-0.458224\pi$
$449$	−7.78946e7	−	7.78946e7i	−0.860535	−	0.860535i	−0.991400	+	0.130865i	$0.958224\pi$
$450$	−4.42723e7	+	4.42723e7i	−0.485842	+	0.485842i
$451$	−1.53578e8			−1.67417
$452$	−2.24287e8	−	2.24287e8i	−2.42879	−	2.42879i
$453$	−2.03660e6	+	2.03660e6i	−0.0219084	+	0.0219084i
$454$	1.72494e8	+	1.72494e8i	1.84334	+	1.84334i
$455$	2.83834e7			0.301321
$456$	−1.70061e8	−	1.70061e8i	−1.79354	−	1.79354i
$457$			5.47335e6i			0.0573462i	0.999589	+	0.0286731i	$0.00912818\pi$
$457$			5.47335e6i			0.0573462i	−0.999589	+	0.0286731i	$0.990872\pi$
$458$	5.62278e7			0.585267
$459$	−2.22018e7			−0.229589
$460$	−3.12647e8			−3.21204
$461$	1.48490e7	−	1.48490e7i	0.151563	−	0.151563i	−0.627253	−	0.778816i	$-0.715821\pi$
$461$	1.48490e7	−	1.48490e7i	0.151563	−	0.151563i	0.778816	+	0.627253i	$0.215821\pi$
$462$	1.74224e8	−	1.74224e8i	1.76678	−	1.76678i
$463$		−	6.06332e7i		−	0.610896i	−0.952209	−	0.305448i	$-0.901194\pi$
$463$		−	6.06332e7i		−	0.610896i	0.952209	−	0.305448i	$-0.0988062\pi$
$464$	4.32088e8	+	8.11083e7i	4.32533	+	0.811916i
$465$	−4.11362e6			−0.0409134
$466$	−2.63669e8	−	2.63669e8i	−2.60556	−	2.60556i
$467$	7.52198e7	+	7.52198e7i	0.738552	+	0.738552i	0.972298	−	0.233745i	$-0.0750982\pi$
$467$	7.52198e7	+	7.52198e7i	0.738552	+	0.738552i	−0.233745	+	0.972298i	$0.575098\pi$
$468$			5.75680e7i			0.561621i
$469$		−	4.80663e7i		−	0.465932i
$470$		−	3.58671e8i		−	3.45464i
$471$	−1.32116e8			−1.26442
$472$	−1.58273e7	+	1.58273e7i	−0.150516	+	0.150516i
$473$		−	1.06673e8i		−	1.00803i
$474$	7.63155e7	−	7.63155e7i	0.716602	−	0.716602i
$475$	1.80540e7	+	1.80540e7i	0.168459	+	0.168459i
$476$	−1.52055e8	+	1.52055e8i	−1.40988	+	1.40988i
$477$			5.96308e7i			0.549434i
$478$	−1.25152e8	−	1.25152e8i	−1.14592	−	1.14592i
$479$	−1.65611e7	+	1.65611e7i	−0.150690	+	0.150690i	−0.778426	−	0.627736i	$-0.783982\pi$
$479$	−1.65611e7	+	1.65611e7i	−0.150690	+	0.150690i	0.627736	+	0.778426i	$0.283982\pi$
$480$	8.80561e8			7.96225
$481$	−1.55766e7	−	1.55766e7i	−0.139971	−	0.139971i
$482$	1.85008e8	−	1.85008e8i	1.65215	−	1.65215i
$483$	9.45062e7	+	9.45062e7i	0.838724	+	0.838724i
$484$	7.57046e6			0.0667707
$485$	1.05599e8	+	1.05599e8i	0.925628	+	0.925628i
$486$		−	2.82152e8i		−	2.45796i
$487$	7.76595e7			0.672369			0.336184	−	0.941796i	$-0.390863\pi$
$487$	7.76595e7			0.672369			0.336184	+	0.941796i	$0.390863\pi$
$488$	−3.39004e7			−0.291706
$489$	−3.77989e7			−0.323261
$490$	1.23392e7	−	1.23392e7i	0.104882	−	0.104882i
$491$	−1.33352e8	+	1.33352e8i	−1.12656	+	1.12656i	−0.135827	+	0.990733i	$0.543369\pi$
$491$	−1.33352e8	+	1.33352e8i	−1.12656	+	1.12656i	−0.990733	+	0.135827i	$0.956631\pi$
$492$			7.69613e8i			6.46215i
$493$	4.84089e7	+	7.07825e7i	0.404002	+	0.590725i
$494$	3.16353e7			0.262417
$495$	−7.76467e7	−	7.76467e7i	−0.640188	−	0.640188i
$496$	9.69605e6	+	9.69605e6i	0.0794602	+	0.0794602i
$497$		−	2.41329e7i		−	0.196580i
$498$		−	3.28503e8i		−	2.65982i
$499$			1.56776e8i			1.26177i	0.775878	+	0.630883i	$0.217307\pi$
$499$			1.56776e8i			1.26177i	−0.775878	+	0.630883i	$0.782693\pi$
$500$	2.34551e8			1.87641
$501$	2.30455e8	−	2.30455e8i	1.83262	−	1.83262i
$502$			8.14416e7i			0.643776i
$503$	−1.28675e8	+	1.28675e8i	−1.01109	+	1.01109i	−0.0111509	+	0.999938i	$0.503550\pi$
$503$	−1.28675e8	+	1.28675e8i	−1.01109	+	1.01109i	−0.999938	+	0.0111509i	$0.996450\pi$
$504$	−2.45615e8	−	2.45615e8i	−1.91851	−	1.91851i
$505$	−6.43837e7	+	6.43837e7i	−0.499922	+	0.499922i
$506$		−	2.32919e8i		−	1.79785i
$507$	1.14085e8	+	1.14085e8i	0.875395	+	0.875395i
$508$	4.47167e7	−	4.47167e7i	0.341097	−	0.341097i
$509$	−9.38524e7			−0.711692			−0.355846	−	0.934545i	$-0.615807\pi$
$509$	−9.38524e7			−0.711692			−0.355846	+	0.934545i	$0.615807\pi$
$510$	2.11787e8	+	2.11787e8i	1.59658	+	1.59658i
$511$	−2.33663e7	+	2.33663e7i	−0.175116	+	0.175116i
$512$	−5.31737e8	−	5.31737e8i	−3.96175	−	3.96175i
$513$	−2.24154e7			−0.166033
$514$	−4.56835e7	−	4.56835e7i	−0.336411	−	0.336411i
$515$			2.06494e8i			1.51177i
$516$	−5.34563e8			−3.89090
$517$	1.98288e8			1.43491
$518$	2.03723e8			1.46572
$519$	5.91768e7	−	5.91768e7i	0.423301	−	0.423301i
$520$	−1.14356e8	+	1.14356e8i	−0.813294	+	0.813294i
$521$		−	1.98386e8i		−	1.40281i	−0.712764	−	0.701404i	$-0.752557\pi$
$521$		−	1.98386e8i		−	1.40281i	0.712764	−	0.701404i	$-0.247443\pi$
$522$	−1.75244e8	+	1.19851e8i	−1.23206	+	0.842616i
$523$	1.04465e8			0.730243			0.365122	−	0.930960i	$-0.381027\pi$
$523$	1.04465e8			0.730243			0.365122	+	0.930960i	$0.381027\pi$
$524$	−1.56282e6	−	1.56282e6i	−0.0108621	−	0.0108621i
$525$	6.04725e7	+	6.04725e7i	0.417907	+	0.417907i
$526$		−	1.55640e8i		−	1.06946i
$527$			2.67465e6i			0.0182741i
$528$			8.48901e8i			5.76707i
$529$	−2.16914e7			−0.146528
$530$	−1.81556e8	+	1.81556e8i	−1.21950	+	1.21950i
$531$		−	6.53614e6i		−	0.0436554i
$532$	−1.53518e8	+	1.53518e8i	−1.01959	+	1.01959i
$533$	−4.67033e7	−	4.67033e7i	−0.308436	−	0.308436i
$534$	3.79206e7	−	3.79206e7i	0.249030	−	0.249030i
$535$		−	7.32399e7i		−	0.478285i
$536$	1.93658e8	+	1.93658e8i	1.25759	+	1.25759i
$537$	2.51780e8	−	2.51780e8i	1.62591	−	1.62591i
$538$	−3.76990e8			−2.42093
$539$	6.82162e6	+	6.82162e6i	0.0435634	+	0.0435634i
$540$	1.24192e8	−	1.24192e8i	0.788703	−	0.788703i
$541$	1.51285e8	+	1.51285e8i	0.955441	+	0.955441i	0.999049	−	0.0436075i	$-0.0138851\pi$
$541$	1.51285e8	+	1.51285e8i	0.955441	+	0.955441i	−0.0436075	+	0.999049i	$0.513885\pi$
$542$	−2.11816e8			−1.33033
$543$	6.91279e6	+	6.91279e6i	0.0431771	+	0.0431771i
$544$		−	5.72535e8i		−	3.55636i
$545$	−3.47531e8			−2.14686
$546$	1.05964e8			0.650996
$547$	−1.02682e8			−0.627380			−0.313690	−	0.949525i	$-0.601565\pi$
$547$	−1.02682e8			−0.627380			−0.313690	+	0.949525i	$0.601565\pi$
$548$	6.63257e7	−	6.63257e7i	0.403033	−	0.403033i
$549$	6.99983e6	−	6.99983e6i	0.0423029	−	0.0423029i
$550$		−	1.49040e8i		−	0.895805i
$551$	4.88745e7	+	7.14635e7i	0.292165	+	0.427198i
$552$	−7.61525e8			−4.52759
$553$	−4.49474e7	−	4.49474e7i	−0.265784	−	0.265784i
$554$	1.02341e8	+	1.02341e8i	0.601895	+	0.601895i
$555$		−	2.10566e8i		−	1.23171i
$556$			8.35581e8i			4.86143i
$557$			2.43070e8i			1.40658i	0.710901	+	0.703292i	$0.248288\pi$
$557$			2.43070e8i			1.40658i	−0.710901	+	0.703292i	$0.751712\pi$
$558$	−6.62191e6			−0.0381137
$559$	3.24395e7	−	3.24395e7i	0.185711	−	0.185711i
$560$		−	9.04377e8i		−	5.14974i
$561$	−1.17084e8	+	1.17084e8i	−0.663148	+	0.663148i
$562$	4.66767e8	+	4.66767e8i	2.62961	+	2.62961i
$563$	8.84388e7	−	8.84388e7i	0.495584	−	0.495584i	−0.414476	−	0.910060i	$-0.636035\pi$
$563$	8.84388e7	−	8.84388e7i	0.495584	−	0.495584i	0.910060	+	0.414476i	$0.136035\pi$
$564$		−	9.93662e8i		−	5.53862i
$565$	1.83990e8	+	1.83990e8i	1.02012	+	1.02012i
$566$	−1.24686e8	+	1.24686e8i	−0.687651	+	0.687651i
$567$	−2.08885e8			−1.14593
$568$	9.72306e7	+	9.72306e7i	0.530588	+	0.530588i
$569$	−4.77712e7	+	4.77712e7i	−0.259316	+	0.259316i	−0.824776	−	0.565460i	$-0.808699\pi$
$569$	−4.77712e7	+	4.77712e7i	−0.259316	+	0.259316i	0.565460	+	0.824776i	$0.308699\pi$
$570$	2.13825e8	+	2.13825e8i	1.15460	+	1.15460i
$571$	1.75931e8			0.945007			0.472503	−	0.881329i	$-0.343350\pi$
$571$	1.75931e8			0.945007			0.472503	+	0.881329i	$0.343350\pi$
$572$	−9.68992e7	−	9.68992e7i	−0.517764	−	0.517764i
$573$			3.64624e8i			1.93812i
$574$	6.10821e8			3.22982
$575$	8.08451e7			0.425256
$576$	7.79950e8			4.08131
$577$	3.08665e7	−	3.08665e7i	0.160679	−	0.160679i	−0.622188	−	0.782868i	$-0.713756\pi$
$577$	3.08665e7	−	3.08665e7i	0.160679	−	0.160679i	0.782868	+	0.622188i	$0.213756\pi$
$578$	−1.31157e8	+	1.31157e8i	−0.679214	+	0.679214i
$579$		−	3.25902e8i		−	1.67900i
$580$	−6.66732e8	−	1.25154e8i	−3.41717	−	0.641445i
$581$	−1.93478e8			−0.986514
$582$	3.94234e8	+	3.94234e8i	1.99979	+	1.99979i
$583$	−1.00371e8	−	1.00371e8i	−0.506529	−	0.506529i
$584$		−	1.88284e8i		−	0.945312i
$585$		−	4.72249e7i		−	0.235887i
$586$		−	3.05102e8i		−	1.51619i
$587$	−1.42761e7			−0.0705823			−0.0352912	−	0.999377i	$-0.511236\pi$
$587$	−1.42761e7			−0.0705823			−0.0352912	+	0.999377i	$0.511236\pi$
$588$	3.41846e7	−	3.41846e7i	0.168151	−	0.168151i
$589$			2.70038e6i			0.0132154i
$590$	1.99004e7	−	1.99004e7i	0.0968958	−	0.0968958i
$591$	−1.41796e8	−	1.41796e8i	−0.686913	−	0.686913i
$592$	−4.96317e8	+	4.96317e8i	−2.39218	+	2.39218i
$593$		−	6.58623e7i		−	0.315844i	−0.987452	−	0.157922i	$-0.949520\pi$
$593$		−	6.58623e7i		−	0.315844i	0.987452	−	0.157922i	$-0.0504795\pi$
$594$	9.25217e7	+	9.25217e7i	0.441453	+	0.441453i
$595$	1.24736e8	−	1.24736e8i	0.592162	−	0.592162i
$596$	7.28825e8			3.44258
$597$	−2.45706e8	−	2.45706e8i	−1.15477	−	1.15477i
$598$	7.08308e7	−	7.08308e7i	0.331222	−	0.331222i
$599$	1.70670e8	+	1.70670e8i	0.794103	+	0.794103i	0.982158	−	0.188055i	$-0.0602184\pi$
$599$	1.70670e8	+	1.70670e8i	0.794103	+	0.794103i	−0.188055	+	0.982158i	$0.560218\pi$
$600$	−4.87284e8			−2.25594
$601$	−1.41450e8	−	1.41450e8i	−0.651597	−	0.651597i	0.301780	−	0.953377i	$-0.402419\pi$
$601$	−1.41450e8	−	1.41450e8i	−0.651597	−	0.651597i	−0.953377	+	0.301780i	$0.902419\pi$
$602$			4.24268e8i			1.94469i
$603$	−7.99739e7			−0.364751
$604$	−1.48144e7			−0.0672316
$605$	−6.21030e6			−0.0280444
$606$	−2.40364e8	+	2.40364e8i	−1.08007	+	1.08007i
$607$	2.04626e8	−	2.04626e8i	0.914946	−	0.914946i	−0.0817099	−	0.996656i	$-0.526038\pi$
$607$	2.04626e8	−	2.04626e8i	0.914946	−	0.914946i	0.996656	+	0.0817099i	$0.0260381\pi$
$608$		−	5.78043e8i		−	2.57187i
$609$	1.63707e8	+	2.39369e8i	0.724794	+	1.05978i
$610$	4.26243e7			0.187788
$611$	6.02995e7	+	6.02995e7i	0.264357	+	0.264357i
$612$	2.52993e8	+	2.52993e8i	1.10371	+	1.10371i
$613$		−	9.46167e7i		−	0.410758i	−0.978683	−	0.205379i	$-0.934157\pi$
$613$		−	9.46167e7i		−	0.410758i	0.978683	−	0.205379i	$-0.0658427\pi$
$614$		−	5.63434e8i		−	2.43410i
$615$		−	6.31339e8i		−	2.71417i
$616$	8.26845e8			3.53738
$617$	5.08538e7	−	5.08538e7i	0.216505	−	0.216505i	−0.590519	−	0.807024i	$-0.701077\pi$
$617$	5.08538e7	−	5.08538e7i	0.216505	−	0.216505i	0.807024	+	0.590519i	$0.201077\pi$
$618$			7.70902e8i			3.26613i
$619$	−3.80776e7	+	3.80776e7i	−0.160545	+	0.160545i	−0.782808	−	0.622263i	$-0.786213\pi$
$619$	−3.80776e7	+	3.80776e7i	−0.160545	+	0.160545i	0.622263	+	0.782808i	$0.286213\pi$
$620$	−1.49614e7	−	1.49614e7i	−0.0627766	−	0.0627766i
$621$	−5.01876e7	+	5.01876e7i	−0.209566	+	0.209566i
$622$			6.11463e8i			2.54097i
$623$	−2.23340e7	−	2.23340e7i	−0.0923641	−	0.0923641i
$624$	−2.58152e8	+	2.58152e8i	−1.06248	+	1.06248i
$625$	−3.04791e8			−1.24843
$626$	−3.92530e8	−	3.92530e8i	−1.60011	−	1.60011i
$627$	−1.18211e8	+	1.18211e8i	−0.479573	+	0.479573i
$628$	−4.80512e8	−	4.80512e8i	−1.94011	−	1.94011i
$629$	−1.36909e8			−0.550148
$630$	3.08822e8	+	3.08822e8i	1.23506	+	1.23506i
$631$			5.48366e7i			0.218264i	0.994027	+	0.109132i	$0.0348071\pi$
$631$			5.48366e7i			0.218264i	−0.994027	+	0.109132i	$0.965193\pi$
$632$	3.62184e8			1.43475
$633$	1.99189e8			0.785332
$634$	−4.01061e8			−1.57378
$635$	−3.66825e7	+	3.66825e7i	−0.143264	+	0.143264i
$636$	−5.02983e8	+	5.02983e8i	−1.95516	+	1.95516i
$637$			4.14893e6i			0.0160516i
$638$	9.32380e7	−	4.96707e8i	0.359030	−	1.91266i
$639$	−4.01528e7			−0.153891
$640$	1.26156e9	+	1.26156e9i	4.81247	+	4.81247i
$641$	−2.05719e8	−	2.05719e8i	−0.781090	−	0.781090i	0.198925	−	0.980015i	$-0.436255\pi$
$641$	−2.05719e8	−	2.05719e8i	−0.781090	−	0.781090i	−0.980015	+	0.198925i	$0.936255\pi$
$642$		−	2.73426e8i		−	1.03332i
$643$			1.56161e8i			0.587406i	0.955897	+	0.293703i	$0.0948877\pi$
$643$			1.56161e8i			0.587406i	−0.955897	+	0.293703i	$0.905112\pi$
$644$			6.87447e8i			2.57384i
$645$	4.38519e8			1.63422
$646$	1.39027e8	−	1.39027e8i	0.515707	−	0.515707i
$647$		−	1.66146e8i		−	0.613447i	−0.951799	−	0.306723i	$-0.900767\pi$
$647$		−	1.66146e8i		−	0.613447i	0.951799	−	0.306723i	$-0.0992326\pi$
$648$	8.41593e8	−	8.41593e8i	3.09298	−	3.09298i
$649$	1.10017e7	+	1.10017e7i	0.0402463	+	0.0402463i
$650$	4.53231e7	−	4.53231e7i	0.165036	−	0.165036i
$651$			9.04500e6i			0.0327843i
$652$	−1.37476e8	−	1.37476e8i	−0.496004	−	0.496004i
$653$	−2.20120e8	+	2.20120e8i	−0.790534	+	0.790534i	−0.981581	−	0.191047i	$-0.938812\pi$
$653$	−2.20120e8	+	2.20120e8i	−0.790534	+	0.790534i	0.191047	+	0.981581i	$0.438812\pi$
$654$	−1.29744e9			−4.63823
$655$	1.28203e6	+	1.28203e6i	0.00456221	+	0.00456221i
$656$	−1.48810e9	+	1.48810e9i	−5.27135	+	5.27135i
$657$	3.88774e7	+	3.88774e7i	0.137088	+	0.137088i
$658$	−7.88643e8			−2.76823
$659$	3.31293e8	+	3.31293e8i	1.15759	+	1.15759i	0.984992	+	0.172603i	$0.0552176\pi$
$659$	3.31293e8	+	3.31293e8i	1.15759	+	1.15759i	0.172603	+	0.984992i	$0.444782\pi$
$660$		−	1.30989e9i		−	4.55621i
$661$	−3.76754e8			−1.30453			−0.652264	−	0.757992i	$-0.726181\pi$
$661$	−3.76754e8			−1.30453			−0.652264	+	0.757992i	$0.726181\pi$
$662$	−8.09890e8			−2.79159
$663$	−7.12110e7			−0.244347
$664$	7.79517e8	−	7.79517e8i	2.66270	−	2.66270i
$665$	1.25936e8	−	1.25936e8i	0.428238	−	0.428238i
$666$		−	3.38959e8i		−	1.14743i
$667$	2.69434e8	+	5.05761e7i	0.907977	+	0.170438i
$668$	1.67635e9			5.62387
$669$	−2.07415e7	−	2.07415e7i	−0.0692727	−	0.0692727i
$670$	−2.43494e8	−	2.43494e8i	−0.809587	−	0.809587i
$671$			2.35644e7i			0.0779990i
$672$		−	1.93617e9i		−	6.38022i
$673$		−	3.02150e8i		−	0.991236i	−0.868541	−	0.495618i	$-0.834942\pi$
$673$		−	3.02150e8i		−	0.991236i	0.868541	−	0.495618i	$-0.165058\pi$
$674$	4.04603e8			1.32145
$675$	−3.21139e7	+	3.21139e7i	−0.104420	+	0.104420i
$676$			8.29864e8i			2.68638i
$677$	−3.17806e8	+	3.17806e8i	−1.02423	+	1.02423i	−0.0245275	+	0.999699i	$0.507808\pi$
$677$	−3.17806e8	+	3.17806e8i	−1.02423	+	1.02423i	−0.999699	+	0.0245275i	$0.992192\pi$
$678$	6.86890e8	+	6.86890e8i	2.20393	+	2.20393i
$679$	2.32191e8	−	2.32191e8i	0.741715	−	0.741715i
$680$			1.00512e9i			3.19661i
$681$	−3.92018e8	−	3.92018e8i	−1.24126	−	1.24126i
$682$	1.11461e7	−	1.11461e7i	0.0351374	−	0.0351374i
$683$	4.54213e8			1.42560			0.712799	−	0.701368i	$-0.247427\pi$
$683$	4.54213e8			1.42560			0.712799	+	0.701368i	$0.247427\pi$
$684$	2.55427e8	+	2.55427e8i	0.798176	+	0.798176i
$685$	−5.44091e7	+	5.44091e7i	−0.169278	+	0.169278i
$686$	−4.62380e8	−	4.62380e8i	−1.43228	−	1.43228i
$687$	−1.27786e8			−0.394106
$688$	−1.03362e9	−	1.03362e9i	−3.17391	−	3.17391i
$689$		−	6.10461e7i		−	0.186638i
$690$	9.57497e8			2.91468
$691$	−1.77570e7			−0.0538190			−0.0269095	−	0.999638i	$-0.508567\pi$
$691$	−1.77570e7			−0.0538190			−0.0269095	+	0.999638i	$0.508567\pi$
$692$	4.30457e8			1.29901
$693$	−1.70729e8	+	1.70729e8i	−0.512989	+	0.512989i
$694$	−3.32795e8	+	3.32795e8i	−0.995630	+	0.995630i
$695$		−	6.85455e8i		−	2.04185i
$696$	−1.62398e9	−	3.04841e8i	−4.81674	−	0.904160i
$697$	−4.10492e8			−1.21229
$698$	3.31508e8	+	3.31508e8i	0.974827	+	0.974827i
$699$	5.99227e8	+	5.99227e8i	1.75453	+	1.75453i
$700$			4.39883e8i			1.28246i
$701$		−	1.80942e8i		−	0.525272i	−0.964895	−	0.262636i	$-0.915408\pi$
$701$		−	1.80942e8i		−	0.525272i	0.964895	−	0.262636i	$-0.0845918\pi$
$702$			5.62719e7i			0.162660i
$703$	−1.38226e8			−0.397854
$704$	−1.31282e9	+	1.31282e9i	−3.76260	+	3.76260i
$705$			8.15134e8i			2.32628i
$706$	6.81871e8	−	6.81871e8i	1.93771	−	1.93771i
$707$	1.41567e8	+	1.41567e8i	0.400592	+	0.400592i
$708$	5.51320e7	−	5.51320e7i	0.155347	−	0.155347i
$709$		−	3.37548e8i		−	0.947103i	−0.880766	−	0.473551i	$-0.842972\pi$
$709$		−	3.37548e8i		−	0.947103i	0.880766	−	0.473551i	$-0.157028\pi$
$710$	−1.22252e8	−	1.22252e8i	−0.341571	−	0.341571i
$711$	−7.47846e7	+	7.47846e7i	−0.208067	+	0.208067i
$712$	1.79966e8			0.498599
$713$	6.04609e6	+	6.04609e6i	0.0166804	+	0.0166804i
$714$	4.65677e8	−	4.65677e8i	1.27935	−	1.27935i
$715$	7.94896e7	+	7.94896e7i	0.217466	+	0.217466i
$716$	1.83147e9			4.98954
$717$	2.84426e8	+	2.84426e8i	0.771635	+	0.771635i
$718$			1.03016e9i			2.78311i
$719$	5.15273e8			1.38628			0.693140	−	0.720803i	$-0.256227\pi$
$719$	5.15273e8			1.38628			0.693140	+	0.720803i	$0.256227\pi$
$720$	−1.50472e9			−4.03143
$721$	4.54037e8			1.21139
$722$	−3.83662e8	+	3.83662e8i	−1.01938	+	1.01938i
$723$	−4.20459e8	+	4.20459e8i	−1.11252	+	1.11252i
$724$			5.02843e7i			0.132500i
$725$	1.72405e8	+	3.23625e7i	0.452414	+	0.0849236i
$726$	−2.31849e7			−0.0605892
$727$	−1.97889e8	−	1.97889e8i	−0.515013	−	0.515013i	0.401045	−	0.916058i	$-0.368647\pi$
$727$	−1.97889e8	−	1.97889e8i	−0.515013	−	0.515013i	−0.916058	+	0.401045i	$0.868647\pi$
$728$	2.51445e8	+	2.51445e8i	0.651701	+	0.651701i
$729$			1.82755e8i			0.471723i
$730$			2.36737e8i			0.608553i
$731$		−	2.85123e8i		−	0.729927i
$732$	1.18086e8			0.301070
$733$	1.84815e8	−	1.84815e8i	0.469273	−	0.469273i	−0.432406	−	0.901679i	$-0.642335\pi$
$733$	1.84815e8	−	1.84815e8i	0.469273	−	0.469273i	0.901679	+	0.432406i	$0.142335\pi$
$734$		−	5.30406e8i		−	1.34128i
$735$	−2.80428e7	+	2.80428e7i	−0.0706251	+	0.0706251i
$736$	−1.29422e9	−	1.29422e9i	−3.24621	−	3.24621i
$737$	1.34613e8	−	1.34613e8i	0.336267	−	0.336267i
$738$		−	1.01630e9i		−	2.52844i
$739$	−1.65378e6	−	1.65378e6i	−0.00409773	−	0.00409773i	0.705055	−	0.709153i	$-0.250922\pi$
$739$	−1.65378e6	−	1.65378e6i	−0.00409773	−	0.00409773i	−0.709153	+	0.705055i	$0.750922\pi$
$740$	7.65839e8	−	7.65839e8i	1.88992	−	1.88992i
$741$	−7.18961e7			−0.176706
$742$	3.99204e8	+	3.99204e8i	0.977199	+	0.977199i
$743$	2.15881e8	−	2.15881e8i	0.526318	−	0.526318i	−0.393155	−	0.919472i	$-0.628616\pi$
$743$	2.15881e8	−	2.15881e8i	0.526318	−	0.526318i	0.919472	+	0.393155i	$0.128616\pi$
$744$	−3.64420e7	−	3.64420e7i	−0.0884879	−	0.0884879i
$745$	−5.97879e8			−1.44592
$746$	1.62682e8	+	1.62682e8i	0.391853	+	0.391853i
$747$			3.21913e8i			0.772285i
$748$	−8.51683e8			−2.03504
$749$	−1.61039e8			−0.383254
$750$	−7.18322e8			−1.70269
$751$	−4.06613e8	+	4.06613e8i	−0.959978	+	0.959978i	−0.999229	−	0.0392518i	$-0.987503\pi$
$751$	−4.06613e8	+	4.06613e8i	−0.959978	+	0.959978i	0.0392518	+	0.999229i	$0.487503\pi$
$752$	1.92132e9	−	1.92132e9i	4.51800	−	4.51800i
$753$		−	1.85088e8i		−	0.433505i
$754$	1.79403e8	−	1.22695e8i	0.418519	−	0.286229i
$755$	1.21527e7			0.0282380
$756$	−2.73073e8	−	2.73073e8i	−0.631995	−	0.631995i
$757$	−7.23274e7	−	7.23274e7i	−0.166731	−	0.166731i	0.618810	−	0.785541i	$-0.287615\pi$
$757$	−7.23274e7	−	7.23274e7i	−0.166731	−	0.166731i	−0.785541	+	0.618810i	$0.787615\pi$
$758$		−	2.21738e8i		−	0.509135i
$759$			5.29343e8i			1.21063i
$760$			1.01478e9i			2.31171i
$761$	5.89186e8			1.33690			0.668450	−	0.743757i	$-0.266958\pi$
$761$	5.89186e8			1.33690			0.668450	+	0.743757i	$0.266958\pi$
$762$	−1.36947e8	+	1.36947e8i	−0.309519	+	0.309519i
$763$			7.64149e8i			1.72030i
$764$	−1.32615e9	+	1.32615e9i	−2.97382	+	2.97382i
$765$	−2.07539e8	−	2.07539e8i	−0.463570	−	0.463570i
$766$	4.66791e7	−	4.66791e7i	0.103857	−	0.103857i
$767$			6.69127e6i			0.0148294i
$768$	2.42321e9	+	2.42321e9i	5.34942	+	5.34942i
$769$	−3.80384e8	+	3.80384e8i	−0.836456	+	0.836456i	−0.988391	−	0.151935i	$-0.951450\pi$
$769$	−3.80384e8	+	3.80384e8i	−0.836456	+	0.836456i	0.151935	+	0.988391i	$0.451450\pi$
$770$	−1.03963e9			−2.27722
$771$	1.03823e8	+	1.03823e8i	0.226532	+	0.226532i
$772$	1.18532e9	−	1.18532e9i	2.57623	−	2.57623i
$773$	2.38925e7	+	2.38925e7i	0.0517277	+	0.0517277i	0.732497	−	0.680770i	$-0.238355\pi$
$773$	2.38925e7	+	2.38925e7i	0.0517277	+	0.0517277i	−0.680770	+	0.732497i	$0.738355\pi$
$774$	7.05908e8			1.52239
$775$	3.86876e6	+	3.86876e6i	0.00831126	+	0.00831126i
$776$			1.87098e9i			4.00392i
$777$	−4.62992e8			−0.986984
$778$	1.23552e9			2.62368
$779$	−4.14441e8			−0.876699
$780$	3.98340e8	−	3.98340e8i	0.839401	−	0.839401i
$781$	6.75858e7	−	6.75858e7i	0.141874	−	0.141874i
$782$		−	6.22559e8i		−	1.30185i
$783$	−1.27117e8	+	8.69365e7i	−0.264800	+	0.181099i
$784$	1.32197e8			0.274330
$785$	3.94180e8	+	3.94180e8i	0.814865	+	0.814865i
$786$	4.78622e6	+	4.78622e6i	0.00985654	+	0.00985654i
$787$			2.39523e8i			0.491386i	0.969348	+	0.245693i	$0.0790155\pi$
$787$			2.39523e8i			0.491386i	−0.969348	+	0.245693i	$0.920984\pi$
$788$		−	1.03144e9i		−	2.10797i
$789$			3.53715e8i			0.720149i
$790$	−4.55388e8			−0.923636
$791$	4.04557e8	−	4.04557e8i	0.817429	−	0.817429i
$792$		−	1.37572e9i		−	2.76921i
$793$	−7.16597e6	+	7.16597e6i	−0.0143700	+	0.0143700i
$794$	−7.32182e8	−	7.32182e8i	−1.46271	−	1.46271i
$795$	4.12613e8	−	4.12613e8i	0.821187	−	0.821187i
$796$		−	1.78729e9i		−	3.54370i
$797$	−5.09083e8	−	5.09083e8i	−1.00557	−	1.00557i	−0.999984	−	0.00558826i	$-0.998221\pi$
$797$	−5.09083e8	−	5.09083e8i	−1.00557	−	1.00557i	−0.00558826	−	0.999984i	$-0.501779\pi$
$798$	4.70156e8	−	4.70156e8i	0.925196	−	0.925196i
$799$	5.29995e8			1.03904
$800$	−8.28147e8	−	8.28147e8i	−1.61747	−	1.61747i
$801$	−3.71599e7	+	3.71599e7i	−0.0723065	+	0.0723065i
$802$	−9.82223e8	−	9.82223e8i	−1.90409	−	1.90409i
$803$	−1.30878e8			−0.252766
$804$	−6.74575e8	−	6.74575e8i	−1.29796	−	1.29796i
$805$		−	5.63936e8i		−	1.08104i
$806$	6.77908e6			0.0129469
$807$	8.56766e8			1.63020
$808$	−1.14073e9			−2.16247
$809$	−3.01544e8	+	3.01544e8i	−0.569515	+	0.569515i	−0.931993	−	0.362477i	$-0.881931\pi$
$809$	−3.01544e8	+	3.01544e8i	−0.569515	+	0.569515i	0.362477	+	0.931993i	$0.381931\pi$
$810$	−1.05817e9	+	1.05817e9i	−1.99113	+	1.99113i
$811$		−	1.06931e8i		−	0.200466i	−0.994964	−	0.100233i	$-0.968041\pi$
$811$		−	1.06931e8i		−	0.200466i	0.994964	−	0.100233i	$-0.0319588\pi$
$812$	−2.75187e8	+	1.46601e9i	−0.513996	+	2.73821i
$813$	4.81384e8			0.895818
$814$	5.70541e8	+	5.70541e8i	1.05782	+	1.05782i
$815$	1.12776e8	+	1.12776e8i	0.208327	+	0.208327i
$816$			2.26899e9i			4.17602i
$817$		−	2.87865e8i		−	0.527866i
$818$			4.79609e8i			0.876250i
$819$	−1.03838e8			−0.189018
$820$	2.29621e9	−	2.29621e9i	4.16457	−	4.16457i
$821$		−	4.72061e8i		−	0.853038i	−0.904479	−	0.426519i	$-0.859740\pi$
$821$		−	4.72061e8i		−	0.853038i	0.904479	−	0.426519i	$-0.140260\pi$
$822$	−2.03125e8	+	2.03125e8i	−0.365720	+	0.365720i
$823$	5.58804e8	+	5.58804e8i	1.00244	+	1.00244i	0.999997	+	0.00244708i	$0.000778930\pi$
$823$	5.58804e8	+	5.58804e8i	1.00244	+	1.00244i	0.00244708	+	0.999997i	$0.499221\pi$
$824$	−1.82930e9	+	1.82930e9i	−3.26967	+	3.26967i
$825$			3.38715e8i			0.603215i
$826$	−4.37568e7	−	4.37568e7i	−0.0776435	−	0.0776435i
$827$	−2.28987e8	+	2.28987e8i	−0.404851	+	0.404851i	−0.879938	−	0.475088i	$-0.842416\pi$
$827$	−2.28987e8	+	2.28987e8i	−0.404851	+	0.404851i	0.475088	+	0.879938i	$0.342416\pi$
$828$	1.14379e9			2.01491
$829$	5.85673e8	+	5.85673e8i	1.02800	+	1.02800i	0.999597	+	0.0284003i	$0.00904132\pi$
$829$	5.85673e8	+	5.85673e8i	1.02800	+	1.02800i	0.0284003	+	0.999597i	$0.490959\pi$
$830$	−9.80119e8	+	9.80119e8i	−1.71413	+	1.71413i
$831$	−2.32586e8	−	2.32586e8i	−0.405303	−	0.405303i
$832$	−7.98462e8			−1.38639
$833$	1.82332e7	+	1.82332e7i	0.0315449	+	0.0315449i
$834$		−	2.55901e9i		−	4.41137i
$835$	−1.37517e9			−2.36208
$836$	−8.59876e8			−1.47169
$837$	−4.80335e6			−0.00819158
$838$	−7.37671e8	+	7.37671e8i	−1.25352	+	1.25352i
$839$	7.30293e8	−	7.30293e8i	1.23655	−	1.23655i	0.275146	−	0.961402i	$-0.411274\pi$
$839$	7.30293e8	−	7.30293e8i	1.23655	−	1.23655i	0.961402	−	0.275146i	$-0.0887263\pi$
$840$			3.39905e9i			5.73482i
$841$	5.54332e8	+	2.15710e8i	0.931927	+	0.362646i
$842$	−1.50664e9			−2.52391
$843$	−1.06080e9	−	1.06080e9i	−1.77072	−	1.77072i
$844$	7.24459e8	+	7.24459e8i	1.20500	+	1.20500i
$845$		−	6.80765e8i		−	1.12831i
$846$			1.31216e9i			2.16709i
$847$			1.36552e7i			0.0224722i
$848$	−1.94511e9			−3.18975
$849$	2.83368e8	−	2.83368e8i	0.463049	−	0.463049i
$850$		−	3.98362e8i		−	0.648666i
$851$	−3.09485e8	+	3.09485e8i	−0.502170	+	0.502170i
$852$	−3.38687e8	−	3.38687e8i	−0.547621	−	0.547621i
$853$	3.63064e8	−	3.63064e8i	0.584973	−	0.584973i	−0.351292	−	0.936266i	$-0.614258\pi$
$853$	3.63064e8	−	3.63064e8i	0.584973	−	0.584973i	0.936266	+	0.351292i	$0.114258\pi$
$854$		−	9.37221e7i		−	0.150476i
$855$	−2.09535e8	−	2.09535e8i	−0.335242	−	0.335242i
$856$	6.48823e8	−	6.48823e8i	1.03444	−	1.03444i
$857$	5.86156e8			0.931259			0.465630	−	0.884980i	$-0.345828\pi$
$857$	5.86156e8			0.931259			0.465630	+	0.884980i	$0.345828\pi$
$858$	2.96758e8	+	2.96758e8i	0.469830	+	0.469830i
$859$	−6.53762e8	+	6.53762e8i	−1.03143	+	1.03143i	−0.0319416	+	0.999490i	$0.510169\pi$
$859$	−6.53762e8	+	6.53762e8i	−1.03143	+	1.03143i	−0.999490	+	0.0319416i	$0.989831\pi$
$860$	1.59492e9	+	1.59492e9i	2.50751	+	2.50751i
$861$	−1.38818e9			−2.17489
$862$	1.76406e9	+	1.76406e9i	2.75418	+	2.75418i
$863$		−	6.53364e8i		−	1.01654i	−0.861199	−	0.508268i	$-0.830286\pi$
$863$		−	6.53364e8i		−	1.01654i	0.861199	−	0.508268i	$-0.169714\pi$
$864$	1.02820e9			1.59418
$865$	−3.53118e8			−0.545597
$866$	5.07690e8			0.781708
$867$	2.98073e8	−	2.98073e8i	0.457368	−	0.457368i
$868$	−3.28971e7	+	3.28971e7i	−0.0503035	+	0.0503035i
$869$		−	2.51757e8i		−	0.383638i
$870$	2.04190e9	+	3.83289e8i	3.10082	+	0.582061i
$871$	8.18720e7			0.123903
$872$	−3.07873e9	−	3.07873e9i	−4.64325	−	4.64325i
$873$	−3.86326e8	−	3.86326e8i	−0.580645	−	0.580645i
$874$		−	6.28548e8i		−	0.941465i
$875$			4.23069e8i			0.631520i
$876$			6.55858e8i			0.975657i
$877$	3.86932e8			0.573636			0.286818	−	0.957985i	$-0.407403\pi$
$877$	3.86932e8			0.573636			0.286818	+	0.957985i	$0.407403\pi$
$878$	9.71727e8	−	9.71727e8i	1.43569	−	1.43569i
$879$			6.93391e8i			1.02097i
$880$	2.53277e9	−	2.53277e9i	3.71662	−	3.71662i
$881$	1.77842e8	+	1.77842e8i	0.260080	+	0.260080i	0.825087	−	0.565006i	$-0.191126\pi$
$881$	1.77842e8	+	1.77842e8i	0.260080	+	0.260080i	−0.565006	+	0.825087i	$0.691126\pi$
$882$	−4.51420e7	+	4.51420e7i	−0.0657922	+	0.0657922i
$883$			1.09682e9i			1.59313i	0.604552	+	0.796566i	$0.293352\pi$
$883$			1.09682e9i			1.59313i	−0.604552	+	0.796566i	$0.706648\pi$
$884$	−2.58998e8	−	2.58998e8i	−0.374921	−	0.374921i
$885$	−4.52266e7	+	4.52266e7i	−0.0652475	+	0.0652475i
$886$	1.22361e9			1.75930
$887$	−8.67903e8	−	8.67903e8i	−1.24366	−	1.24366i	−0.958473	−	0.285183i	$-0.907946\pi$
$887$	−8.67903e8	−	8.67903e8i	−1.24366	−	1.24366i	−0.285183	−	0.958473i	$-0.592054\pi$
$888$	1.86538e9	−	1.86538e9i	2.66396	−	2.66396i
$889$	8.06573e7	+	8.06573e7i	0.114799	+	0.114799i
$890$	−2.26279e8			−0.320977
$891$	−5.84998e8	−	5.84998e8i	−0.827031	−	0.827031i
$892$		−	1.50876e8i		−	0.212581i
$893$	5.35093e8			0.751407
$894$	−2.23206e9			−3.12387
$895$	−1.50241e9			−2.09566
$896$	2.77391e9	−	2.77391e9i	3.85628	−	3.85628i
$897$	−1.60974e8	+	1.60974e8i	−0.223037	+	0.223037i
$898$			1.73528e9i			2.39629i
$899$	1.04732e7	+	1.53138e7i	0.0144146	+	0.0210767i
$900$	7.31887e8			1.00396
$901$	−2.68279e8	−	2.68279e8i	−0.366785	−	0.366785i
$902$	1.71065e9	+	1.71065e9i	2.33099	+	2.33099i
$903$		−	9.64214e8i		−	1.30951i
$904$			3.25989e9i			4.41263i
$905$		−	4.12498e7i		−	0.0556514i
$906$	4.53698e7			0.0610074
$907$	1.59485e8	−	1.59485e8i	0.213746	−	0.213746i	−0.592111	−	0.805857i	$-0.701705\pi$
$907$	1.59485e8	−	1.59485e8i	0.213746	−	0.213746i	0.805857	+	0.592111i	$0.201705\pi$
$908$		−	2.85157e9i		−	3.80914i
$909$	2.35542e8	−	2.35542e8i	0.313600	−	0.313600i
$910$	−3.16152e8	−	3.16152e8i	−0.419538	−	0.419538i
$911$	8.98696e8	−	8.98696e8i	1.18866	−	1.18866i	0.211222	−	0.977438i	$-0.432256\pi$
$911$	8.98696e8	−	8.98696e8i	1.18866	−	1.18866i	0.977438	−	0.211222i	$-0.0677442\pi$
$912$			2.29082e9i			3.02000i
$913$	−5.41849e8	−	5.41849e8i	−0.711977	−	0.711977i
$914$	6.09656e7	−	6.09656e7i	0.0798447	−	0.0798447i
$915$	−9.68702e7			−0.126452
$916$	−4.64764e8	−	4.64764e8i	−0.604708	−	0.604708i
$917$	2.81893e6	−	2.81893e6i	0.00365575	−	0.00365575i
$918$	2.47298e8	+	2.47298e8i	0.319663	+	0.319663i
$919$	3.03240e8			0.390696			0.195348	−	0.980734i	$-0.437416\pi$
$919$	3.03240e8			0.390696			0.195348	+	0.980734i	$0.437416\pi$
$920$	2.27208e9	+	2.27208e9i	2.91783	+	2.91783i
$921$			1.28049e9i			1.63907i
$922$	−3.30795e8			−0.422052
$923$	4.11058e7			0.0522755
$924$	−2.88018e9			−3.65093
$925$	−1.98033e8	+	1.98033e8i	−0.250214	+	0.250214i
$926$	−6.75370e8	+	6.75370e8i	−0.850568	+	0.850568i
$927$		−	7.55438e8i		−	0.948330i
$928$	−2.24190e9	−	3.27806e9i	−2.80525	−	4.10179i
$929$	5.56024e8			0.693500			0.346750	−	0.937958i	$-0.387285\pi$
$929$	5.56024e8			0.693500			0.346750	+	0.937958i	$0.387285\pi$
$930$	4.58201e7	+	4.58201e7i	0.0569648	+	0.0569648i
$931$	1.84086e7	+	1.84086e7i	0.0228125	+	0.0228125i
$932$			4.35883e9i			5.38422i
$933$		−	1.38964e9i		−	1.71103i
$934$		−	1.67569e9i		−	2.05661i
$935$	6.98664e8			0.854739
$936$	4.18359e8	−	4.18359e8i	0.510178	−	0.510178i
$937$			5.61348e8i			0.682359i	0.939998	+	0.341180i	$0.110826\pi$
$937$			5.61348e8i			0.682359i	−0.939998	+	0.341180i	$0.889174\pi$
$938$	−5.35393e8	+	5.35393e8i	−0.648730	+	0.648730i
$939$	8.92084e8	+	8.92084e8i	1.07748	+	1.07748i
$940$	−2.96468e9	+	2.96468e9i	−3.56939	+	3.56939i
$941$			3.58307e8i			0.430018i	0.976612	+	0.215009i	$0.0689780\pi$
$941$			3.58307e8i			0.430018i	−0.976612	+	0.215009i	$0.931022\pi$
$942$	1.47159e9	+	1.47159e9i	1.76049	+	1.76049i
$943$	−9.27925e8	+	9.27925e8i	−1.10657	+	1.10657i
$944$	2.13203e8			0.253442
$945$	2.24011e8	+	2.24011e8i	0.265444	+	0.265444i
$946$	−1.18819e9	+	1.18819e9i	−1.40350	+	1.40350i
$947$	3.55244e8	+	3.55244e8i	0.418289	+	0.418289i	0.884614	−	0.466324i	$-0.154422\pi$
$947$	3.55244e8	+	3.55244e8i	0.418289	+	0.418289i	−0.466324	+	0.884614i	$0.654422\pi$
$948$	−1.26161e9			−1.48081
$949$	−3.98001e7	−	3.98001e7i	−0.0465678	−	0.0465678i
$950$		−	4.02194e8i		−	0.469099i
$951$	9.11472e8			1.05975
$952$	2.21004e9			2.56147
$953$	1.18323e9			1.36707			0.683534	−	0.729919i	$-0.260442\pi$
$953$	1.18323e9			1.36707			0.683534	+	0.729919i	$0.260442\pi$
$954$	6.64205e8	−	6.64205e8i	0.764993	−	0.764993i
$955$	1.08789e9	−	1.08789e9i	1.24903	−	1.24903i
$956$			2.06894e9i			2.36796i
$957$	−2.11897e8	+	1.12884e9i	−0.241763	+	1.28794i
$958$	3.68937e8			0.419619
$959$	1.19634e8	+	1.19634e8i	0.135644	+	0.135644i
$960$	−5.39684e9	−	5.39684e9i	−6.09994	−	6.09994i
$961$		−	8.86925e8i		−	0.999348i
$962$			3.47004e8i			0.389771i
$963$			2.67941e8i			0.300027i
$964$	−3.05846e9			−3.41406
$965$	−9.72359e8	+	9.72359e8i	−1.08204	+	1.08204i
$966$		−	2.10534e9i		−	2.33556i
$967$	5.27844e8	−	5.27844e8i	0.583748	−	0.583748i	−0.352183	−	0.935931i	$-0.614560\pi$
$967$	5.27844e8	−	5.27844e8i	0.583748	−	0.583748i	0.935931	+	0.352183i	$0.114560\pi$
$968$	−5.50162e7	−	5.50162e7i	−0.0606547	−	0.0606547i
$969$	−3.15961e8	+	3.15961e8i	−0.347266	+	0.347266i
$970$		−	2.35247e9i		−	2.57756i
$971$	−8.67449e7	−	8.67449e7i	−0.0947515	−	0.0947515i	0.658142	−	0.752894i	$-0.271343\pi$
$971$	−8.67449e7	−	8.67449e7i	−0.0947515	−	0.0947515i	−0.752894	+	0.658142i	$0.771343\pi$
$972$	−2.33219e9	+	2.33219e9i	−2.53960	+	2.53960i
$973$	−1.50717e9			−1.63616
$974$	−8.65020e8	−	8.65020e8i	−0.936158	−	0.936158i
$975$	−1.03004e8	+	1.03004e8i	−0.111132	+	0.111132i
$976$	2.28329e8	+	2.28329e8i	0.245590	+	0.245590i
$977$	5.24515e8			0.562437			0.281219	−	0.959644i	$-0.409261\pi$
$977$	5.24515e8			0.562437			0.281219	+	0.959644i	$0.409261\pi$
$978$	4.21028e8	+	4.21028e8i	0.450085	+	0.450085i
$979$		−	1.25096e8i		−	0.133320i
$980$	−2.03986e8			−0.216731
$981$	1.27141e9			1.34672
$982$	2.97071e9			3.13708
$983$	6.78242e7	−	6.78242e7i	0.0714043	−	0.0714043i	−0.670503	−	0.741907i	$-0.733922\pi$
$983$	6.78242e7	−	6.78242e7i	0.0714043	−	0.0714043i	0.741907	+	0.670503i	$0.233922\pi$
$984$	5.59295e9	−	5.59295e9i	5.87024	−	5.87024i
$985$			8.46123e8i			0.885370i
$986$	2.49212e8	−	1.32763e9i	0.259979	−	1.38499i
$987$	1.79231e9			1.86407
$988$	−2.61489e8	−	2.61489e8i	−0.271134	−	0.271134i
$989$	−6.44524e8	−	6.44524e8i	−0.666270	−	0.666270i
$990$			1.72975e9i			1.78270i
$991$			1.03546e9i			1.06392i	0.846768	+	0.531962i	$0.178545\pi$
$991$			1.03546e9i			1.06392i	−0.846768	+	0.531962i	$0.821455\pi$
$992$		−	1.23868e8i		−	0.126889i
$993$	1.84060e9			1.87980
$994$	−2.68807e8	+	2.68807e8i	−0.273704	+	0.273704i
$995$			1.46617e9i			1.48839i
$996$	−2.71532e9	+	2.71532e9i	−2.74817	+	2.74817i
$997$	−6.45255e8	−	6.45255e8i	−0.651097	−	0.651097i	0.302160	−	0.953257i	$-0.402292\pi$
$997$	−6.45255e8	−	6.45255e8i	−0.651097	−	0.651097i	−0.953257	+	0.302160i	$0.902292\pi$
$998$	1.74627e9	−	1.74627e9i	1.75679	−	1.75679i
$999$		−	2.45872e8i		−	0.246611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.7.c.a.12.1	✓	28
29.17	odd	4	inner	29.7.c.a.17.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.7.c.a.12.1	✓	28	1.1	even	1	trivial
29.7.c.a.17.1	yes	28	29.17	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.1386 - 11.1386i) q^{2} +(25.3142 + 25.3142i) q^{3} +184.138i q^{4} -151.054i q^{5} -563.931i q^{6} -332.137 q^{7} +(1338.17 - 1338.17i) q^{8} +552.618i q^{9} +O(q^{10})\)	\(q+(-11.1386 - 11.1386i) q^{2} +(25.3142 + 25.3142i) q^{3} +184.138i q^{4} -151.054i q^{5} -563.931i q^{6} -332.137 q^{7} +(1338.17 - 1338.17i) q^{8} +552.618i q^{9} +(-1682.54 + 1682.54i) q^{10} +(-930.174 - 930.174i) q^{11} +(-4661.31 + 4661.31i) q^{12} -565.734i q^{13} +(3699.55 + 3699.55i) q^{14} +(3823.82 - 3823.82i) q^{15} -18026.0 q^{16} +(-2486.23 - 2486.23i) q^{17} +(6155.41 - 6155.41i) q^{18} +(-2510.14 - 2510.14i) q^{19} +27814.8 q^{20} +(-8407.80 - 8407.80i) q^{21} +20721.7i q^{22} -11240.3 q^{23} +67749.5 q^{24} -7192.43 q^{25} +(-6301.50 + 6301.50i) q^{26} +(4464.96 - 4464.96i) q^{27} -61159.1i q^{28} +(-23970.3 - 4499.53i) q^{29} -85184.3 q^{30} +(-537.894 - 537.894i) q^{31} +(115141. + 115141. i) q^{32} -47093.2i q^{33} +55386.3i q^{34} +50170.8i q^{35} -101758. q^{36} +(27533.5 - 27533.5i) q^{37} +55919.1i q^{38} +(14321.1 - 14321.1i) q^{39} +(-202137. - 202137. i) q^{40} +(82553.3 - 82553.3i) q^{41} +187303. i q^{42} +(57340.5 + 57340.5i) q^{43} +(171280. - 171280. i) q^{44} +83475.4 q^{45} +(125202. + 125202. i) q^{46} +(-106586. + 106586. i) q^{47} +(-456313. - 456313. i) q^{48} -7333.71 q^{49} +(80113.8 + 80113.8i) q^{50} -125874. i q^{51} +104173. q^{52} +107906. q^{53} -99467.1 q^{54} +(-140507. + 140507. i) q^{55} +(-444457. + 444457. i) q^{56} -127085. i q^{57} +(216878. + 317115. i) q^{58} -11827.6 q^{59} +(704111. + 704111. i) q^{60} +(-12666.7 - 12666.7i) q^{61} +11982.8i q^{62} -183545. i q^{63} -1.41137e6i q^{64} -85456.6 q^{65} +(-524554. + 524554. i) q^{66} +144718. i q^{67} +(457809. - 457809. i) q^{68} +(-284540. - 284540. i) q^{69} +(558834. - 558834. i) q^{70} +72659.2i q^{71} +(739498. + 739498. i) q^{72} +(70351.3 - 70351.3i) q^{73} -613370. q^{74} +(-182071. - 182071. i) q^{75} +(462213. - 462213. i) q^{76} +(308946. + 308946. i) q^{77} -319035. q^{78} +(135328. + 135328. i) q^{79} +2.72290e6i q^{80} +628913. q^{81} -1.83906e6 q^{82} +582524. q^{83} +(1.54819e6 - 1.54819e6i) q^{84} +(-375555. + 375555. i) q^{85} -1.27739e6i q^{86} +(-492888. - 720692. i) q^{87} -2.48947e6 q^{88} +(67243.4 + 67243.4i) q^{89} +(-929801. - 929801. i) q^{90} +187902. i q^{91} -2.06977e6i q^{92} -27232.7i q^{93} +2.37445e6 q^{94} +(-379168. + 379168. i) q^{95} +5.82943e6i q^{96} +(-699082. + 699082. i) q^{97} +(81687.4 + 81687.4i) q^{98} +(514031. - 514031. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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